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| [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn) | | [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn) | ||
| Spectral order invariant and obstruction to Stein fillability | | Spectral order invariant and obstruction to Stein fillability | ||
− | | In this joint work with Ca\ugatay Kutluhan, Jeremy Van Horn- Morris and Andy Wand, we define an invariant of contact structures in dimension three arising from introducing a filtration on the boundary operator in Heegaard Floer homology. This invariant takes values in the set $\Z_{\geq0}\cup\{\infty\}$. It is zero for overtwisted contact structures, ∞ for Stein fillable contact structures, non-decreasing under Legendrian surgery, and computable from any supporting open book decomposition. I will give the definition and discuss computability of the invariant. As an application, we give an easily computable obstruction to Stein fillability on closed contact 3-manifolds with non-vanishing Ozsváth-Szabó contact class. | + | | In this joint work with Ca\ugatay Kutluhan, Jeremy Van Horn- Morris and Andy Wand, we define an invariant of contact structures in dimension three arising from introducing a filtration on the boundary operator in Heegaard Floer homology. This invariant takes values in the set $\Z_{\geq0}\cup\{\infty\}$. It is zero for overtwisted contact structures, ∞ for Stein fillable contact structures, non-decreasing under Legendrian surgery, and computable from any supporting open book decomposition. I will give the definition and discuss computability of the invariant. As an application, we give an easily computable obstruction to Stein fillability on closed contact 3-manifolds with non-vanishing Ozsváth-Szabó contact class. {{math|{{mathbb|Z}} |
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| June 23 | | June 23 |
Revision as of 18:01, 11 June 2020
Regensburg low-dimensional geometry and topology seminar
The seminar takes place on Zoom (see information below) every Tuesday at 16:00 CET (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).
Upcoming Talks
Date | Speaker | Title | Abstract |
---|---|---|---|
June 16 | Gordana Matic (Univ. of Georgia/MPIM Bonn) | Spectral order invariant and obstruction to Stein fillability | Template:Mathbb |
June 23 | Lisa Piccirillo (MIT) | tba | tba |
June 30 | Kathryn Mann (Cornell) | tba | tba |
July 7 | Mikhail Khovanov (Columbia University) | Introduction to foam evaluation and its uses | tba |
July 14 | Claudius Zibrowius (UBC Vancouver) | tba | tba |
July 21 | Marc Lackenby (University of Oxford) | tba | tba |
The program is also contained in the RLGTS Google Calendar. To receive announcements by email, sign up to our mailing list.
Zoom information
Zoom Meeting ID: 924 2829 6353
The password is the answer to the following riddle (lower case, singular, no article): As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold).
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.
Past Talks (with slides and videos for download)
Date | Speaker | Title | Downloads | Abstract |
---|---|---|---|---|
May 5 | Peter Kronheimer (Harvard) | Genus versus double-points for immersed surfaces | Video | If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions. |
May 12 | Danny Calegari (University of Chicago) | Taut foliations leafwise branch cover the 2-sphere | Video, Slides | A co-oriented foliation of an oriented 3-manifold is taut if and only if there is a map from the 3-manifold to the 2-sphere which is a branched cover when restricted to each leaf. I shall give two proofs of this theorem and explain its relation to theorems of Ghys and Donaldson. |
May 19 | Richard Webb (University of Manchester) | Quasimorphisms on diffeomorphism groups | Video, Slides | I will explain how to construct an unbounded quasimorphism on the group of isotopically-trivial diffeomorphisms of a surface of positive genus. As a corollary the commutator length and fragmentation norm are both (stably) unbounded, which solves a problem of Burago--Ivanov--Polterovich. The proof uses a new hyperbolic graph on which these groups act by isometries, which is inspired by techniques from mapping class groups. This is joint work with Jonathan Bowden and Sebastian Hensel. |
May 26 | Zhenkun Li (MIT) | Instanton Floer homology and the depth of taut foliations | Video, Slides | Sutured manifold hierarchy is a powerful tool introduced by Gabai to study the topology of 3-manifolds. The length of a sutured manifold hierarchy gives us a measurement of how complicated the sutured manifold is. Also, using this tool, Gabai proved the existence of finite depth taut foliations. However, he didn’t discuss how finite the depth could be.
Sutured Instanton Floer homology was introduced by Kronheimer and Mrowka and is defined on balanced sutured manifolds. In this talk, I will explain how sutured instanton Floer homology could offer us bounds for the minimal length of a sutured hierarchy and the minimal depth of a foliation on a fixed balanced sutured manifold. |
June 2 | no talk (pentecoste) | |||
June 9 | Boyu Zhang (Princeton) | Instanton Floer homology for tangles and applications in Khovanov homology | Video, Slides | In this talk, I will present an excision formula for singular instanton Floer homology where the excision surfaces intersect the singular locus. This formula allows us to define an instanton Floer homology theory for sutured manifolds with tangles. Similar to the non-singular case, the instant Floer homology for tangles is non-vanishing on taut manifolds with tangles and detects trivial products. As applications, we prove several detection results for Khovanov homology. This is joint work with Yi Xie. |