This is the website for the joint topology seminar between Duke, NCSU and UNC. The seminar will normally meet on selected Tuesdays with the location rotating between Duke, NCSU and UNC. An informal pretalk seminar aimed at graduate students will also be held before some talks. The webpage for this seminar can be found here
Please contact one of the organizers to be added to our mailing list.
| Speaker | Date/Time | Location | Title |
| Alejandro Adem (University of British Columbia) |
Aug 23 4:30PM | NCSU SAS 4201 |
Commutativity, Bundles and K-theory | Jem Hom (Georgia Institute of Technology) |
Sept 27 3:00PM | NCSU SAS 2012 |
Knot concordance in homology spheres |
| Dror Bar-Natan (University of Toronto) |
Oct 10 3:30PM | UNC Phillips 247 |
A Poly-Time Knot Polynomial Via Solvable Approximation |
| Adam Levine (Princeton University) |
Nov 15 4:00PM | Duke Physics 119 |
Heegaard Floer invariants for homology $S^1 \times S^3$s |
| Joanna Nelson (Columbia/Barnard) |
Nov 15 5:15PM | Duke Physics 119 |
An integral lift of cylindrical contact homology |
| Tobias Ekholm (Uppsala University and Institut Mittag-Leffler) |
Nov 29 4:30PM | Duke Physics 119 |
Wrapped Floer cohomology and Legendrian surgery |
Abstracts
August 23, 2016 at 4:30 pm
Alejandro Adem
Commutativity, Bundles and K-theory
Abstract: In this talk I will describe a new cohomology theory constructed out of commuting unitary matrices. I will discuss its role in bundle theory and homotopy theory.
September 27, 2016 at 3:00 pm
Jen Hom
Knot concordance in homology spheres
Abstract: The knot concordance group C consists of knots in S^3 modulo concordance. We consider C_Z, the group of knots in homology spheres that bound homology balls modulo homology bordisms of pairs. Matsumoto asked if the natural map from C to C_Z is an isomorphism. Adam Levine answered this question in the negative by showing the map is not surjective. We show that the image of C in C_Z is of infinite index. This is joint work with Adam Levine and Tye Lidman.
October 10, 2016 at 3:30 pm
Dror Bar-Natan
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/.
November 15, 2016 at 4:00 pm
Adam Levine
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 certain types of 3-manifolds, including those obtained as a connected sum of a rational homology 3-sphere and any number of copies of $S^1 \times S^2$. We also give similar obstructions to embeddings in certain open 4-manifolds, including exotic $\mathbb{R}^4$s. This is joint work with Danny Ruberman.
November 15, 2016 at 5:15 pm
Joanna Nelson
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 tensored with $\mathbb{Q}$ recovers the classical cylindrical contact homology, now with the guarantee of well-definedness and invariance. This integral lift of contact homology also contains interesting torsion information.
November 29, 2016 at 4:30 pm
Tobias Ekholm
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 to the topology of Lagrangian fillings of Legendrian submanifolds. The talk reports on joint work with Y. Lekili.