Time and venueThe LSU Virtual Topology Seminar meets in 233 Lockett Hall, at 3:30 pm CT on Wednesdays.
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Schedule The schedule is updated throughout the academic year, and only confirmed speakers are listed below.| Date | Speaker | Institution | Title |
|---|---|---|---|
| Sep 6, 2017 | Peter Lambert-Cole | Georgia Institute of Technology | Conway mutation and knot Floer homology |
| Sep 13, 2017 | Mike Wong | Louisiana State University | An unoriented skein exact triangle for grid homology |
| Sep 27, 2017 | John Etnyre | Georgia Institute of Technology | Contact surgeries and symplectic fillings |
| Oct 4, 2017 | Mike Wong | Louisiana State University | An unoriented skein exact relation for tangle Floer homology |
| Oct 18, 2017 | Robin Koytcheff | University of Louisiana at Lafayette | Homotopy string links, configuration spaces, and the kappa invariant |
| Oct 25, 2017 | Yilong Wang | Ohio State University | Integrality for SO(p)_2-TQFTs |
| Nov 8, 2017 | Mike Wong | Louisiana State University | Ends of moduli spaces in bordered Floer homology I |
| Nov 15, 2017 | Mike Wong | Louisiana State University | Ends of moduli spaces in bordered Floer homology II |
| Feb 21, 2018 | Shea Vela-Vick | Louisiana State University | Knot Floer homology and fibered knots |
| Feb 28, 2018 | Ivan Levcovitz | CUNY Graduate Center | Coarse geometry of right-angled Coxeter groups |
| Mar 7, 2018 | Bülent Tosun | University of Alabama | Obstructing Stein structures on contractible 4-manifolds |
| Mar 14, 2018 | Ina Petkova | Dartmouth College | Knot Floer homology and the gl(1|1) link invariant |
| Mar 21, 2018 | Adam Levine | Duke University | Piecewise-linear disks and spheres in 4-manifolds |
| Apr 25, 2018 | Miriam Kuzbary | Rice University | Perspectives on link concordance groups |
Abstracts
Date Sep 6, 2017
Speaker Peter Lambert-Cole
Title Conway mutation and knot Floer homology
Abstract Mutant knots are notoriously hard to distinguish. Many, but not all, knot invariants take the same value on mutant pairs. Khovanov homology with coefficients in Z/2Z is known to be mutation-invariant, while the bigraded knot Floer homology groups can distinguish mutants such as the famous Kinoshita–Terasaka and Conway pair. However, Baldwin and Levine conjectured that delta-graded knot Floer homology, a singly-graded reduction of the full invariant, is preserved by mutation. In this talk, I will give a new proof that Khovanov homology mod 2 is mutation-invariant. The same strategy can be applied to delta-graded knot Floer homology and proves the Baldwin–Levine conjecture for mutations on a large class of tangles.
Date Sep 13, 2017
Speaker Mike Wong
Title An unoriented skein exact triangle for grid homology
Abstract Like the Jones and Alexander polynomials, Khovanov and knot Floer homology (HFK) both satisfy an oriented and an unoriented skein exact triangle. Manolescu (2007) proved the unoriented triangle for HFK over Z/2Z. In this talk, we will give a combinatorial proof of the same using grid homology (GH), which is isomorphic to knot Floer homology. This gives rise to a cube-of-resolutions complex that calculates GH-tilde. If time permits, we will outline the generalisation to the case over Z, and an application to quasi-alternating links. No prior experience with the subject is needed, as a brief introduction to grid homology will be given.
Date Sep 27, 2017
Speaker John Etnyre
Title Contact surgeries and symplectic fillings
Abstract It is well known that all contact manifolds can be obtained from the standard contact structure on the 3-sphere by contact surgery on a Legendrian link. What is not so well understood is what properties of a contact structure are preserved by positive contact surgeries (the case for negative contact surgeries is fairly well understood now). In this talk we will discuss some new results about positive contact surgeries and in particular completely characterize when contact r surgery is symplectically fillable when r is in (0,1].
Date Oct 4, 2017
Speaker Mike Wong
Title An unoriented skein exact relation for tangle Floer homology
Abstract Two weeks ago, we talked about an unoriented skein exact triangle for grid homology, which generalizes a result of Manolescu. In this talk, we prove that an analogous skein relation is satisfied by the Petkova–Vertesi tangle Floer homology. Tangle Floer homology is a tangle invariant that satisfies a pairing theorem, recovering the knot Floer homology of a link obtained by gluing tangles. The skein relation for tangle Floer homology, together with the pairing theorem, recovers a version of Manolescu's result. This exhibits the unoriented skein relation of knot Floer homology as a local, rather than global, property. Again, no prior knowledge is necessary for the talk, as a brief introduction to tangle Floer homology will be given. This is joint work with Ina Petkova.
Date Oct 18, 2017
Speaker Robin Koytcheff
Title Homotopy string links, configuration spaces, and the kappa invariant
Abstract A link is an embedding of disjoint circles in space. A link homotopy is a path between two links where distinct components may not pass through each other, but where a component may pass through itself. In the 1990s, Koschorke conjectured that link homotopy classes of n-component links are distinguished by the kappa invariant. This invariant is essentially the map that a link induces on configuration spaces of n points. In joint work with F. Cohen, Komendarczyk, and Shonkwiler, we proved an analogue of this conjecture for string links. A key ingredient is a multiplication on maps of configuration spaces, akin to concatenation of loops in a space. This approach is related to recent joint work with Budney, Conant, and Sinha on finite-type knot invariants and the Taylor tower for the space of knots.
Date Oct 25, 2017
Speaker Yilong Wang
Title Integrality for SO(p)_2-TQFTs
Abstract Representation theory of quantum groups at roots of unity give rise to modular tensor categories hence TQFTs, and the 3-manifold invariants from such constructions are known to be algebraic integers. In this talk, I will introduce the SO(p)_2-TQFT as an example of the above construction, and I will present our results on the integral lattices of the SO(p)_2-TQFT in genus 1 and one-punctured torus.
Date Nov 8, 2017
Speaker Mike Wong
Title Ends of moduli spaces in bordered Floer homology I
Abstract Bordered Floer homology is an invariant associated to 3-manifolds with parametrized boundary, created by Lipshitz, Ozsvath, and Thurston as an extension of Heegaard Floer homology. In this framework, we associate a differential graded algebra A(F) to each surface, and an A-infinity module CF^(Y) to each bordered 3-manifold Y. The module CF^(Y) satisfies a structural equation that should be thought of as the analogue of the condition d^2=0 for chain complexes, obtained by considering ends of moduli spaces that appear in the definition of CF^(Y). In two consecutive expository talks, we will discuss specific examples that illustrate how these ends of moduli spaces match up in pairs. As a starting point, in this talk, we will first focus on the case of grid homology, a specialization of Heegaard Floer homology. No prior knowledge is necessary, as a brief introduction to grid homology will be given.
Date Nov 15, 2017
Speaker Mike Wong
Title Ends of moduli spaces in bordered Floer homology II
Abstract This is the second in two consecutive talks about the ends of moduli spaces in Bordered Floer homology. Bordered Floer homology is an invariant associated to 3-manifolds with parametrized boundary, created by Lipshitz, Ozsvath, and Thurston as an extension of Heegaard Floer homology. In this framework, we associate a differential graded algebra A(F) to each surface, and an A-infinity module CF^(Y) to each bordered 3-manifold Y. The module CF^(Y) satisfies a structural equation that should be thought of as the analogue of the condition d^2=0 for chain complexes, obtained by considering ends of moduli spaces that appear in the definition of CF^(Y). In the talk last week, we discussed how these ends of moduli spaces match up in pairs in grid homology. In this talk, we will focus on the situation in bordered Floer homology, for both type A and type D structures.
Date Feb 21, 2018
Speaker Shea Vela-Vick
Title Knot Floer homology and fibered knots
Abstract We prove that the knot Floer homology of a fibered knot is nontrivial in its next-to-top Alexander grading. Immediate applications include a new proof that L-space knots prime and a classification of knots 3-manifolds with rank 3 knot Floer homology. We will also discuss a numerical refinement of the Ozsvath–Szabo contact invariant. This is joint work with John Baldwin.
Date Feb 28, 2018
Speaker Ivan Levcovitz
Title Coarse geometry of right-angled Coxeter groups
Abstract A main goal of geometric group theory is to understand finitely generated groups up to a coarse equivalence (quasi-isometry) of their Cayley graphs. Right-angled Coxeter groups (RACGs for short), in particular, are important classical objects that have been unexpectedly linked to the theory of hyperbolic 3-manifolds through recent results, including those of Agol and Wise. I will give a background on the relevant geometric group theory, RACGs and what is currently known regarding the quasi-isometric classification of RACGs. I will then describe a new computable quasi-isometry invariant, the hypergraph index, and its relation to other invariants such as divergence and thickness.
Date Mar 7, 2018
Speaker Bülent Tosun
Title Obstructing Stein structures on contractible 4-manifolds
Abstract A Stein manifold is a complex manifold with particularly nice convexity properties. In real dimensions above 4, existence of a Stein structure is essentially a homotopical question, but for 4-manifolds the situation is more subtle. An important question that has been circulating among contact and symplectic topologist for some time asks: whether every contractible smooth 4-manifold admits a Stein structure? In this talk we will provide examples that answer this question negatively. Moreover, along the way we will provide new evidence to a closely related fascinating conjecture of Gompf, which asserts that a nontrivial Brieskorn homology sphere, with either orientation, cannot be embedded in complex 2-space as the boundary of a Stein submanifold. This is a joint work with Tom Mark.
Date Mar 14, 2018
Speaker Ina Petkova
Title Knot Floer homology and the gl(1|1) link invariant
Abstract The Reshetikhin–Turaev construction for the standard representation of the quantum group gl(1|1) sends tangles to C(q)-linear maps in such a way that a knot is sent to its Alexander polynomial. After a brief review of this construction, I will give an introduction to tangle Floer homology – a combinatorial generalization of knot Floer homology which sends tangles to (homotopy equivalence classes of) bigraded dg bimodules. Finally, I will discuss how to see tangle Floer homology as a categorification of the Reshetikhin–Turaev invariant. This is joint work with Alexander Ellis and Vera Vertesi.
Date Mar 21, 2018
Speaker Adam Levine
Title Piecewise-linear disks and spheres in 4-manifolds
Abstract We discuss a variety of problems related to the existence of piecewise-linear (PL) embedded surfaces in smooth 4-manifolds. We give the first known example of a smooth, compact 4-manifold which is homotopy equivalent to the 2-sphere but for which the homotopy equivalence cannot be realized by a PL embedding. We also show that the PL concordance group of knots in homology 3-spheres is infinitely generated and contains elements of infinite order. This is joint work with Jen Hom and Tye Lidman.
Date Apr 25, 2018
Speaker Miriam Kuzbary
Title Perspectives on link concordance groups
Abstract The knot concordance group has been the subject of much study since its introduction by Ralph Fox and John Milnor in 1966. One might hope to generalize the notion of a concordance group to links; however, the immediate generalization to the set of links up to concordance does not form a group since connected sum of links is not well-defined. In this talk, I will discuss two notions of a link concordance group: the string link concordance group due to Le Dimet in 1988 and one due to Matthew Hedden and myself based on the knotification construction of Peter Ozsvath and Zoltan Szabo. I will present invariants for studying these groups coming from Heegaard–Floer homology and a new group theoretic invariant for studying concordance of knots inside in certain types of 3-manifold, as well a preliminary result involving more classical link concordance invariants.