Quantum Topology Seminar
Jun Yoshida
The university of Tokyo
A cobordism realizing crossing change on sl(2) tangle homology and a categorified Vassiliev skein relation
Abstract: arXiv information: https://arxiv.org/abs/2005.12664
In this talk, we discuss degree 0 crossing change on Khovanov homology in terms of cobordisms.
Namely, using Bar-Natan's formalism of Khovanov homology, we introduce a sum of cobordisms that yields a morphism on complexes of two diagrams of crossing change, which we call the "genus-one morphism.”
We prove that the morphism is invariant under the moves of double points in tangle diagrams.
As a consequence, in the spirit of Vassiliev theory, taking iterated mapping cones, we obtain an invariant for singular tangles that extending sl(2) tangle homology; examples include Lee homology, Bar-Natan homology, and Naot's universal Khovanov homology as well as Khovanov homology with arbitrary coefficients.
We also verify that the invariant satisfies categorified analogues of Vassiliev skein relation and the FI relation.
This is a joint work with Noboru Ito (National Institute of Technology, Ibaraki College).
Thursday July 23, 2020 at 4:00 PM in Zoom