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September 2016

Jen Hom (Georgia Tech), Triangle Topology Seminar

September 27, 2016 @ 2:00 pm - 4:00 pm

Pre-talk: SAS 2229 2-2:45 Title: The knot concordance group Abstract: The set of knots in S^3 under the operation of connected sum forms a monoid. By quotienting by an equivalence relation called concordance, we obtain the knot concordance group. We will discuss ways of understanding the structure of this group and introduce some concordance invariants coming from Heegaard Floer theory.   Seminar talk: SAS 2102 3:00-4:00 Title: Knot concordance in homology spheres Abstract: The knot concordance group C consists of knots…

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October 2016

Dror Bar-Natan, Triangle Topology Seminar

October 10, 2016 @ 3:30 pm - 5:00 pm

Title: A Poly-Time Knot Polynomial Via Solvable Approximation Abstract: I will construct the first poly-time-computable knot polynomial since Alexander's (1928) by using some new commutator-calculus techniques and a Lie algebra ${\mathfrak g}_1$ which is at the same time solvable and an approximation of the simple Lie algebra $sl_2$. Slides for the talk can be found at http://www.math.toronto.edu/drorbn/Talks/UNC-1610/.

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November 2016

Adam Levine (Princeton University), Triangle Topology Seminar

November 15, 2016 @ 4:00 pm - 5:00 pm

Title:  Heegaard Floer invariants for homology $S^1 \times S^3$s Abstract: Using Heegaard Floer homology, we construct a numerical invariant for any smooth, oriented 4-manifold $X$ with the homology of $S^1 \times S^3$. Specifically, we show that for any smoothly embedded 3-manifold $Y$ representing a generator of $H_3(X)$, a suitable version of the Heegaard Floer $d$ invariant of $Y$, defined using twisted coefficients, is a diffeomorphism invariant of $X$. We show how this invariant can be used to obstruct embeddings of…

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Joanna Nelson (Columbia/Barnard), Triangle Topology Seminar

November 15, 2016 @ 5:15 pm - 6:15 pm

Title:  An integral lift of cylindrical contact homology Abstract: I will discuss joint work with Hutchings which gives a rigorous construction of cylindrical contact homology via geometric methods. This talk will highlight our use of non-equivariant constructions, automatic transversality, and obstruction bundle gluing. Together these yield a nonequivariant homological contact invariant which is expected to be isomorphic to $SH^+$ under suitable assumptions. By making use of family Floer theory we obtain an $S^1$-equivariant theory defined over $\mathbb{Z}$ coefficients, which when…

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Tobias Ekholm, Triangle Topology Seminar

November 29, 2016 @ 4:30 pm - 5:00 pm

Title: Wrapped Floer cohomology and Legendrian surgery Abstract: We first review the relation between wrapped Floer cohomology of co-core disks after Lagrangian handle attachment and the Legendrian DGA of the corresponding attaching spheres. Then we discuss a generalization of this result to the partially wrapped setting where the Legendrian dga should be enriched with loop space coefficients, and describe several cases when explicit calculations are possible via parallel copies or local coefficient systems. We also discuss applications of these ideas…

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