A whittled complex for the Khovanov homology of torus braids

Seminar: 
Quantum Topology and Field Theory
Event time: 
Thursday, January 29, 2026 - 4:30pm
Location: 
KT 801
Speaker: 
Christine Lee
Speaker affiliation: 
Texas State University
Event description: 

We give an algorithm to reduce the number of generators of the Khovanov chain complex of torus braids $(\sigma_1\sigma_2 \dots\sigma_{n−1})^k$ on $n$ strands. I will begin the talk with context on the stable Khovanov homology of torus links leading to the open question of the structure of their homology theory, as well as potential applications to open questions concerning the colored Jones polynomial. Next I will discuss our work, joint with Carmen Caprau, Nicolle Gonzalez, and Radmila Sazdanovic, using Bar-Natan Gaussian elimination, that gives our whittled complex $\mathcal{FT}_n^k$. The whittled complex is homotopy-equivalent to the original Khovanov chain complex but with a reduced number of generators. After sketching the proof, I will end the talk discussing related future projects.