Date of Award
5-12-2024
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
Advisor(s)
Stephan Wehrli
Second Advisor
Jay Hubisz
Keywords
Khovanov;knot theory;link cobordisms;movie moves;odd Khovanov homology
Subject Categories
Mathematics | Physical Sciences and Mathematics
Abstract
Odd Khovanov Homology is a homological invariant of knots and links that permits a Bar-Natan category presentation. In this dissertation, we extend the odd Khovanov bracket to link cobordisms and prove that our construction is functorial up to sign. We then build an odd Khovanov theory for dotted link cobordisms. Out of the dotted theory, a module structure on the odd Khovanov homology of a diagram over the exterior algebra of the diagram’s coloring group arises. We finish by using our functoriality result to prove that if n is even or if the knot has even framing, then the odd Khovanov homology of the n-cable of a knot admits an action of the Hecke algebra H(q2, n) at q = i.
Access
Open Access
Recommended Citation
Migdail-Smith, Jacob, "The Functoriality of Odd Khovanov Homology up to Sign and Applications" (2024). Dissertations - ALL. 1900.
https://surface.syr.edu/etd/1900
