Date of Award
Summer 7-16-2021
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
Advisor(s)
Wehrli, Stephan
Second Advisor
Miller, Claudia
Keywords
Knot Theory
Subject Categories
Mathematics | Physical Sciences and Mathematics
Abstract
We introduce two monoidal supercategories: the odd dotted Temperley-Lieb category TLo,•(δ), which is a generalization of the odd Temperley-Lieb category studied by Brun-dan and Ellis in [5], and the odd annular Bar-Natan category BNo(A), which generalizes the odd Bar-Natan category studied by Putyra in [16]. We then show there is an equivalence of categories between them if δ=0. We use this equivalence to better understand the action of the Lie superalgebra gl(1|1) on the odd Khovanov homology of a knot in a thickened annulus found by Grigsby and Wehrli in [7].
Access
Open Access
Recommended Citation
Necheles, Casey, "Odd annular Bar-Natan Category and Gl(1|1)" (2021). Dissertations - ALL. 1345.
https://surface.syr.edu/etd/1345
