# Columbia Geometric Topology Seminar

Fall 2021

Organizers: Kyle Hayden, Siddhi Krishna
The GT seminar typically meets on Fridays at 2:00pm Eastern time via the Zoom link above. (The password is `math').

Other area seminars. Our e-mail list. Archive of previous semesters

## Fall 2021

Date Time (Eastern) Speaker Title

September 17

11 am  (Note nonstandard time)

Proper actions of 3-manifold groups on finite product of quasi-trees

September 24

2 pm

The Khovanov homology of slice disks

October 1

2 pm

October 8

2 pm

October 15

2 pm

October 22

2 pm

Jonathan Zung

October 29

November 5

November 12

November 19

2 pm

December 3

December 10

## Abstracts

Wenyuan Yang, Peking University

Title: Proper actions of 3-manifold groups on finite product of quasi-trees

Abstract: Let M be a compact, connected, orientable 3-manifold. In this talk, I will study when the fundamental group of M acts properly on a finite product of quasi-trees. Our main result is that this is so exactly when M does not contain Sol and Nil geometries. In addition, if there is no $\widetilde{SL(2, \mathbb{R})}$ geometry either, then the orbital map is a quasi-isometric embedding of $\pi_1(M)$. This is called property (QT) by Bestvina-Bromberg-Fujiwara, who established it for residually finite hyperbolic groups and mapping class groups. The main step of our proof is to show property (QT) for the classes of Croke-Kleiner admissible groups and of  relatively hyperbolic groups under natural assumptions. Accordingly, this yields that graph 3-manifold and mixed 3-manifold groups have property (QT). This represents joint work with N.T. Nguyen and S.Z. Han.

Isaac Sundberg, Bryn Mawr College

Abstract: A smooth, oriented surface that is properly embedded in the 4-ball can be regarded as a cobordism between the links it bounds, namely, the empty link and its boundary in the 3-sphere. To such link cobordisms, there is an associated linear map between the Khovanov homology groups of the boundary links, and moreover, these maps are invariant, up to sign, under boundary-preserving isotopy of the surface. In this talk, we review these maps and use their invariance to understand the existence and uniqueness of slice disks and other surfaces in the 4-ball. This reflects joint work with Jonah Swann and, separately, with Kyle Hayden.

Gage Martin, Boston College

Joshua Howie, UC Davis

Marissa Loving, Georgia Tech

Jonathan Zung, Princeton University

Valeriano AielloUniversität Bern, Mathematisches Institut

Cameron Rudd, University of Illinois Urbana-Champaign