İstanbul Contact Geometry and Topology Workshop

 

June 7 - June 10, 2010

İstanbul, Turkey


Invited Speakers:

Kenneth Lee Baker, University of Miami

Vincent Colin, Université de Nantes

David Gabai, Princeton University

Hansjörg Geiges, Universität zu Köln

Paolo Ghiggini, Université de Nantes

Jeremy Van Horn-Morris, American Institute of Mathematics

 

The workshop is hosted by İstanbul Center for Mathematical Sciences (IMBM) in Boğaziçi University south campus.

The workshop is supported by Boğaziçi University, Tübitak Feza Gürsey Institute and Tübitak Project No: 107T896.

The workshop organizers are Sinem Çelik Onaran, Ferit Öztürk. For more information send an e-mail to ferit.ozturk@boun.edu.tr or sinem.onaran@boun.edu.tr

 

Program

Schedule

List of Registered Participants

 

How to get to … (first read this)

How to get to IMBM

How to get to Kennedy Lodge and Guest house no:5

How to get to Dormitory no:3

How to get to Boğaziçi University South Campus

How to get to Feza Gürsey Institute

ALL howto's IN PDF

 

 

Program

OPENING TALK

 

David Gabai

  Volumes of hyperbolic 3-manifolds

We outline a proof (with R. Meyerhoff and P. Milley) that the Weeks manifold is the lowest volume closed orientable hyperbolic 3-manifold. Along the way we discuss a number of beautiful and simple ideas needed to understand the topology and geometry of low dimensional manifolds.

 

 

MINI-COURSES

 

Kenneth Lee Baker

  Rational open books and contact structures

The notion of an open book naturally generalizes to the situation where the binding is rationally null homologous. These rational open books support contact structures too. We will survey their behaviours under the operations of Dehn surgery, cabling, and Hopf stabilization.

 

Vincent Colin

  Reeb vector field and open book decompositions

In dimension 3, when a contact form \alpha is adapted to an open book decomposition, the first return map of its Reeb vector field on a page gives a surface diffeomorphism h. The periodic orbits of the Reeb vector field then correspond to the binding curves and the periodic points of h. We will explain how one can use the dynamical properties of h to compute the cylindrical contact homology of  \alpha. We will treat a special case which turns out to be the general one, when h is isotopic to a pseudo-Anosov homeomorphism. This is a joint work with Ko Honda.

 

Hansjörg Geiges

  Contact structures on 5-manifolds

 

Paolo Ghiggini

  Tight contact structures on the Brieskorn spheres and contact invariants

Classifying tight contact structures on Seifert 3-manifolds has been a respectable business for the last ten years, and a lot of progress on this subject has been achieved thank to the effort of several people. However a family of Seifert manifolds denoted by - \Sigma(2,3,6n-1) has proved to be particularly stubborn, and its contact topology has been completely understood only recently in a joint work of Jeremy Van Horn-Morris and myself. In my lectures I will outline the classification of the tight contact structures on - \Sigma(2,3,6n-1) and  the main tool used in the proof, namely  Heegaard Floer homology with twisted coefficients. I will also discuss the importance of this family of three-manifold in the development of three-dimensional contact topology.

 

Jeremy Van Horn-Morris  

 Planar open books and symplectic fillings
Recently, Wendl showed that any planar open book extends to a Lefschetz fibration on a symplectic filling of a compatible contact structure.  We use this to establish uniqueness of symplectic fillings of certain Lens spaces, generalizing work of McDuff and Lisca, and to obstruct fillings of certain contact structures on Seifert fibered spaces. This is joint work with O. Plamenevskaya.

 

 

TALKS and SHORT TALKS

 

Elif Dalyan - Open Book Decompositions of Links Quotient Singularities
In this talk we discuss the open book decompositions of links of quotient surface singularities that support the corresponding unique Milnor fillable contact structures. The page-genus of these Milnor open books are minimal among all Milnor open books supporting the unique Milnor fillable contact structures. That minimal page-genus is called the Milnor genus. We also discuss whether the Milnor genus is equal to the support genus for links of quotient surface singularities. We show that for many types of the quotient surface singularities the Milnor genus is equal to the support genus of the corresponding contact structure. For the remaining we are able to find an upper bound for the support genus.

 

Çağrı Karakurt - Ozsváth-Szabó Contact Invariant and Stein Cobordisms
We will discuss a practical method to calculate c^+, a Floer theoretic invariant of contact structures defined by Ozsváth and Szabó, on certain  plumbed 3-manifolds. The method uses only formal TQFT properties of Heegaard-Floer theory and seems to be carried out in other kinds of Floer homologies, particularly the monopole Floer homology introduced by Kronheimer and Mrowka. Several applications of this formalism will be discussed if the time permits.

 

Elif Medetoğulları - A survey on classification of tight contact structures on Seifert fibered 3-manifolds
Classification of tight contact structures on Seifert fibered 3-manifolds has been an interesting problem for years. There are many techniques such as Convex Surface Theory, Legendrian Surgery, Heegaard Floer Homology, Open Book Decompositions that can be used to find the upper or lower bounds to distinguish tight contact structures. The classification of tight contact structures has been (almost) completed for Seifert fibered 3 manifolds over S^2 with fiber less than or equal to three. In this talk we try to give a short survey on this classification and extend some results to certain Seifert fibered 3 manifold over S^2 with four singular fibers.

 

David Shea Vela Vick  Legendrian contact homology and nondestabilizability
In this talk, I'll discuss some joint work with Clayton Shonkwiler on the relationship between nondestabilizability of Legendrian knots and the vanishing or nonvanishing of Legendrian contact homology.  As an interesting example, I'll present an elementary proof using contact homology that the knot type m(10_161)  contains a nondestabilizable Legendrian representative whose Thurston-Bennequin invariant is nonmaximal.  I'll also speculate a bit about a conjecture of Ng stating that the Legendrian contact homology of a nondestabilizable Legendrian knot should never vanish.

 

Chris Wendl  On symplectic cobordisms between contact manifolds
I will describe some recent progress in understanding the partial order on the category of contact manifolds defined via existence of symplectic cobordisms. In dimension three in particular, it begins to appear that "most" pairs of contact manifolds (excepting obvious obstructions such as symplectic non-fillability) can be related to each other by non-exact symplectic cobordisms, which can be used to obtain much simpler new proofs of various non-fillability results. In contrast, exact symplectic cobordisms display much more rigidity, as demonstrated by an infinite hierarchy of obstructions defined via Symplectic Field Theory.

 

Schedule

 

 

Monday

Tuesday

Wednesday

Thursday

 

9:00-9:30

Registration

Lecture 1 - Baker

Lecture 3 - Ghiggini

Lecture 5 - Colin

 

9:30-10:30

Opening talk - Gabai

11:00-12:30

Lecture 1 - Baker

Lecture 2 - Geiges

Lecture 4 - Van Horn-Morris

Lecture 4 - Van Horn-Morris

12:30-14:30

Lunch

Lunch

Lunch

Lunch

14:30-16:00

Lecture 2 - Geiges

Lecture 3 - Ghiggini

14:30-15:30 Wendl

Lecture 5 - Colin

16:30-17:00

Short talk - Medetoğulları

Short talk - Dalyan

16:00-17:00 Karakurt

Short talk - Vela-Vick

 

 

 List of Registered Participants

 

 

 

Bahar Acu, METU

Mustafa Korkmaz, METU

Anar Akhmedov, University of Minnesota

Laurent La Fuente-Gravy, Université Libre de Bruxelles

Hülya Argüz, METU

Ana García Lecuona, Pisa University      

Aykut Arslan, Michigan State University

Daniel Mathews, Université de Nantes

İnanç Baykur, Brandeis University

Elif Medetoğulları, Atılım Üniversitesi

Ahmet Beyaz, METU

Hiraku Nozawa, ENS-Lyon

Mohan Bhupal, METU

Mehmetçik Pamuk, METU

Barış Coşkunuzer, Koç Üniversitesi

Julian Pook, Université Libre de Bruxelles

Elif Dalyan, Hitit Üniversitesi

Anahita Eslami Rad, Université Libre de Bruxelles

Yvonne Deuster, Universität zu Köln

Nermin Salepci, Université de Pau                                     

Sinan Eden, Boğaziçi Üniversitesi

Sheila (Margherita) Sandon, Université de Nantes

Tolga Etgü, Koç Üniversitesi

Leili Shahriyari, Johns Hopkins University

Steven Frankel, Caltech

Çağlar Uyanık, METU

Marco Golla, University of Cambridge

Anne Vaugon, Université de Nantes

Yusuf Gören, Boğaziçi Üniversitesi

Sibel Sular, Balıkesir Üniversitesi

Özgür İnce, University of Rochester

David Shea Vela-Vick, Columbia University                       

Çağrı Karakurt, Michigan State University

Rafael Torres, Caltech

Vladimir Krouglov, Institute of Math NAS of Ukraine

Chris Wendl, Humboldt-Universität zu Berlin

Hee Jung Kim, Max-Planck Institute for Math

Rumen Zarev, Columbia University

Mirko Klukas, Universität zu Köln

Naïm Zénaïdi, Université Libre de Bruxelles

 

 

How to get to … (first read this)

 

İstanbul is a very large city however it has an extensive public transportation network. The fare for transportation is low. Getting from one place to the other may take long. Do not get intimidated. Be patient. Depending on the route you choose, you will either take a metro, a Metrobüs, a bus, a Dolmuş, a HAVAŞ shuttle, a taxi or several of these. Here are some general tips:

 

Divide the price in liras by 2 to convert it to Euros and by 1,5 to convert to US Dollars.

 

You can pay the fare on a bus. It costs normally 1,50-1,70 Liras (0,75-0,85 Euros) unless otherwise stated below. You must buy a token for a metro and for a Metrobüs in advance which costs 1,50 Liras. You might by an electronic card/ticket ELBİL which consists of 5 tickets and costs 7,50 Liras. You cannot buy an ELBİL on a bus.

 

Although there is a transfer discount, that does not apply if you pay on the bus or if you use an ELBİL.

 

Cabs are usually trustworthy. Yet always make sure that the taxi driver turns the meter on.

 

The trip durations given below are on the average. There might be drastic traffic jams.

 

İstanbul Atatürk Airport (IST) and Boğaziçi University South Campus are on the European side of İstanbul.

 

IMBM, Kennedy Lodge and Guest House No: 5 are in the South Campus.

 

Sabiha Gökçen International Airport and Feza Gürsey Institute are on the Asian side of İstanbul.

 

 

How to get to IMBM

 

IMBM is situated in Boğaziçi University South Campus. Follow the red path in Map.1 below to reach the Center from the main entrance of the South Campus.

Map.1

 

How to get to Kennedy Lodge and Guest House no:5

 

Both are in the South Campus. Kennedy Lodge is marked with the orange circle while Guest House no: 5 is marked with white circle in the Map.1 above. On the white path there are stairs. You may ask your way to the gate keepers of the Campus.

 

How to get to Dormitory no:3

 

This building is situated in the North campus. Once you reach the main gate of the South Campus, follow the orange route shown in the Map.2 below. You may ask your way to the gate keepers of the North Campus. Tell that you are going to Üçüncü Yurt (pronounce Ütchündjü Yurt, read all letters).

Map.2

 

How to get to Boğaziçi University South Campus

 

FROM THE İSTANBUL ATATÜRK AIRPORT TO SOUTH CAMPUS (IST) -- This airport is on the European side as well as Boğaziçi University. There are various ways to get to the campus.

 

1) HAVAŞ + BUS (convenient): Go out of the arrival hall. In front of the building take the shuttle called HAVAŞ to Taksim. It costs 10 liras (5 Euros). It takes around 30-45 minutes to reach Taksim, which is the last stop. Where you get off is shown in the Map.3 below with a red circle. Go to the green circle. Take the bus 559C which goes to Rumelihisarüstü. You can pay on the bus. A ticket costs 1,5 Liras. Tell the driver to drop you at the gate of the South Campus (say Ghünei Kampüs). It takes around 30 minutes to get there. Get off and use the campus map above.

Map.3

 

2) METRO + METROBÜS + BUS (fast, cheapest): Follow the METRO signs in the airport. This is the first stop of the metro. You must buy a token or an ELBİL of 5 tickets. Take the metro and get off at the third station, Ataköy-Şirinevler. This trip takes several minutes. Then change to Metrobüs. This is nothing but a bus on a dedicated track. Take number 34 going to Zincirlikuyu. You can pay on the bus. A ticket costs 1,5 Liras. Get off in Zincirlikuyu, the last stop. It takes around 40 minutes to get there. Follow the signs that reads Sarıyer. Up the stairs there are several bus stops. Take the bus 559C which goes to Rumelihisarüstü. Tell the driver to drop you at the gate of the South Campus (say Ghünei Kampüs). It takes around 15 minutes to get there. Get off and use the Map.1 of the South Campus above.

 

3) TAXI (easy, cheap if you are several people): Go out of the arrival hall. In front of the building take one of the (yellow) cabs. Tell the driver that you want to go to “Boazitchi Üniversitesi Ghünei Kampüs” (read all the letters). It takes around 45 minutes to get to the campus and costs 35-45 Liras (18-22 Euros).

 

FROM SABIHA GÖKÇEN INTERNATIONAL AIRPORT TO SOUTH CAMPUS(SAW) -- This airport is on the Asian side while the university is on the European side.

 

1) BUS + TAXI: Go out of the arrival hall. In front of the building take the bus number E3. It reads Sabiha Gökçen Havalimanı-4. Levent Metro. You can pay on the bus. A ticket costs 4,5 Liras. You will get off at the last stop. The trip takes more than an hour and even more depending on the traffic. On the way you will pass across Bosphorus. As soon as you get off from the bus, use the underground passage to get across the street. At the other side take a (yellow) cab. Tell the driver to take you to Boazitchi Üniversitesi Ghünei Kampüs” (read all the letters). It takes around 15 minutes to get to the campus and costs around 10 Liras (5 Euros).

 

2) HAVAŞ + TAXI: Go out of the arrival hall. In front of the building take the shuttle called HAVAŞ to Taksim. It costs 13 Liras (6,5 Euros). Get off at Kavacık. The trip takes nearly an hour and even more depending on the traffic. As soon as you get off, take a (yellow) cab which will go in the same direction as the shuttle and eventually pass across Bosphorus. Tell the driver to take you to “Boazitchi Üniversitesi Ghünei Kampüs” (read all the letters). It takes around 15 minutes to get to the campus and costs around 15 Liras (7,5 Euros).

 

How to get to Feza Gürsey Institute

 

FROM THE ISTANBUL ATATÜRK AIRPORT TO FEZA GÜRSEY (IST) -- This airport is on the European side while the institute is on the Asian side. There are various ways to get to the institute.
See http://www.gursey.gov.tr/visit.php?m=visit for alternative routes.

 

1)      METRO + METROBÜS + TAXI (fastest): Follow the METRO signs in the airport. This is the first stop of the metro. You must buy a token (1,5 Liras) or an ELBİL. Take the metro and get off at the third station, Ataköy-Şirinevler. This trip takes several minutes. Then change to Metrobüs. This is nothing but a bus on a dedicated track. Take number 34 going to Zincirlikuyu. You can pay on the bus. A ticket costs 1,5 Liras. Get off in Edirnekapı or at some further stop. On the same platform take number 34A going in the same direction. You will not pay again. Get off at the stop Boğazköprüsü; this is the first stop on the Asian side after Bosphorus. The trip with the metrobüs takes around one hour. Leave the highway by taking the stairs to the lower road. Take a (yellow) cab. Tell the driver to take you to “Feza Ghürsei Enstitüsü” at “Kandilli Rasathanesi” (read all the letters). It takes around 15 minutes to get there. Normally the cab should follow the red route in the Map.4 and Map.5 below. It goes for a while along Bosphorus and then takes the road uphill just after Kuleli. The Map.5 shows the portion of the route from Kuleli to the Institute enlarged. The trip with the cab takes around 20 minutes and costs like 10 Liras (5 Euros).

 Map.4

 

Map.5

 

2) METRO + METROBÜS + BUS or DOLMUŞ (fast, cheap): Follow the METRO signs in the airport. This is the first stop of the metro. You must buy a token (1,5 liras) or an ELBİL. Take the metro and get off at the third station, Ataköy-Şirinevler. This trip takes several minutes. Then change to Metrobüs. This is nothing but a bus on a dedicated track. Take number 34 going to Zincirlikuyu. You can pay on the bus. A ticket costs 1,5 Liras. Get off in Edirnekapı or at some further stop. On the same platform take number 34A going in the same direction. You will not pay again. Get off at the stop Boğazköprüsü; this is the first stop on the Asian side after Bosphorus. The trip with the metrobüs takes around one hour. Leave the highway by taking the stairs to the lower road. Follow the white path in the Map.6 below to get to the bus stop marked. At that stop take a bus or a dolmuş. The bus number is 15R and reads Üsküdar-Rasathane. A ticket costs 1,5 Liras. Dolmuş is a small bus (one third of a bus) for 14 people seated. The fare is around 1,5 Liras. In both cases, tell the driver to drop you near “Feza Ghürsei Enstitüsü” next to “Kandilli Rasathanesi” (read all the letters). It takes around 25 minutes to get there. Both the bus and the dolmuş follow the white route in the Map.4 and Map.5 above. The end of the white route is the bus stop. The Map.5 shows the last portion of the route enlarged. The driver can tell you which direction to go as soon as you get off. You have to get across the street and go downhill. Ask to local people where “Feza Ghürsei” is or use the local map at http://www.gursey.gov.tr/visit.php?m=visit#institute.

 Map.6

 

3) TAXI (expensive): Go out of the arrival hall. In front of the building take one of the (yellow) cabs. Tell the driver that you want to go to the Asian side, to Feza Ghürsei Enstitüsü” near “Kandilli Rasathanesi (read all the letters). It takes more than an hour and costs more than 50 Liras (25 Euros). The cab is going to pass across the Bosphorus. Hence they may charge more than it has to be. Besides, the distance is a lot and they might take the liberty to make it longer by choosing this or that bridge. It might cost up to 70 Liras. A little bit chaotic.

 

FROM SABIHA GÖKÇEN INTERNATIONAL AIRPORT TO FEZA GÜRSEY (SAW) -- This airport is on the Asian side as well as the institute.

 

1) BUS + TAXI: Go out of the arrival hall. In front of the building take the bus number E3. It reads Sabiha Gökçen Havalimanı-4. Levent Metro. You can pay on the bus. A ticket costs 4,5 liras. Get off at Kavacık. The trip takes nearly an hour or even more depending on the traffic. As soon as you get off, take a (yellow) cab. Tell the driver to take you to “Feza Ghürsei Enstitüsü” near “Kandilli Rasathanesi” (read all the letters). The cab should turn immediately right and pass over and across the highway to the other side and go downhill, leaving the highway behind. It takes more or less 20 minutes to get to the institute and costs around 20 Liras (10 Euros). Normally the cab should follow either the red route or the white one in the Map.7 below. The red one is shorter.

 

2) HAVAŞ + TAXI: Go out of the arrival hall. In front of the building take the shuttle called HAVAŞ to Taksim. It costs 13 Liras (6,5 Euros). Get off at Kavacık. The trip takes nearly an hour or even more depending on the traffic. As soon as you get off, take a (yellow) cab. Tell the driver to take you to “Feza Ghürsei Enstitüsü” near “Kandilli Rasathanesi” (read all the letters). The cab should turn immediately right and pass over and across the highway to the other side and go downhill, leaving the highway behind. It takes more or less 20 minutes to get to the institute and costs around 20 Liras (10 Euros). Normally the cab should follow either the red route or the white one in the Map.7 below. The white one is shorter.

 Map.7