Quantum Topology Seminar
Scott Carter
Professor Emeritus at the University of South Alabama.
From knotted graphs to foams, exchangers, abstract tensors, and sh-algebra cocycles.
Abstract: Following V. Lebed, we define a structure called a shalgebra. It has two binary operations that satisfy four conditions. An example is a group with multiplication and conjugation as the operations. The axioms mimic moves to knotted travalent graphs, or more precisely handlebody knots in 3-space. The moves are of type IH, IY, YI, and III. We study these moves and how they extrapolate to a family of eight moves to embedded foams in 4-space. The moves correspond to cocycle conditions for the shalgebra and they can be used to define a system of abstract tensor equations that shalgebra cocycles provide a solution for.
The talk is based upon joint work with Kamada, and independently Lebed and Yang as well as earlier work with Ishii, Saito, and Tanaka.
JSCQuantTop20210527.key
https://arxiv.org/pdf/2101.10361.pdf
https://arxiv.org/pdf/1506.08271.pdf
https://arxiv.org/pdf/1711.06215.pdf
Thursday May 27, 2021 at 12:00 PM in Zoom