Topology Seminar- Torsion in Thin Regions of Khovanov Homology

The next talk in the Greater Washington Topology Seminar is on Friday, November 6 from 1pm to 2pm EDT and will be held virtually via Zoom. 

1. October 2, 2020: Louis H. Kauffman (University of Illinois at Chicago and Novosibirsk State University)

2. October 9, 2020: Charles Frohman (University of Iowa)

3. October 16, 2020: Thang T. Q. Lê (Georgia Institute of Technology)

4. October 23, 2020: Pierrick Bousseau (ETH Zurich)

5. October 30, 2020: Micah Chrisman (Ohio State University)

6. November 6, 2020: Alex Chandler (University of Vienna)

7. November 13, 2020: Boštjan Gabrovšek (University of Ljubljana)

8. November 20, 2020: Razvan Gelca (Texas Tech University)

9. December 4, 2020: Helen Wong (Claremont McKenna College) 

Speaker: Alex Chandler 

Title: Torsion in Thin Regions of Khovanov Homology

Abstract: In the integral Khovanov homology of links, the presence of odd torsion is rare. Homologically thin links, that is links whose Khovanov homology is supported on two adjacent diagonals, are known to contain only 2-torsion. In this paper, we prove a local version of this result. If the Khovanov homology of a link is supported on two adjacent diagonals over a range of homological gradings, and the Khovanov homology satisfies some other mild restrictions on the boundary of this range, then the Khovanov homology of that link has only 2-torsion over that range of homological gradings. These conditions are then shown to be met by an infinite family of 3-braids, strictly containing all 3-strand torus links, thus giving a partial answer to Sazdanovic and Przytycki's conjecture that 3-braids have only 2-torsion in Khovanov homology. We also give explicit computations of integral Khovanov homology for all links in this family.
 

The Zoom information is listed below (it is the same as last time): 

Topic: GW Topology Seminar 

Join Zoom Meeting

Meeting ID: 951 840 9059

Password: The last name of the Fields Medalist famous for his work on von Neumann algebras and knot polynomials; first letter capitalized.