|
Organizers |
Quantization of the annular Khovanov homology
by
Krzysztof Putyra
University of Zurich
Coauthors: Anna Beliakova, Stephan M. Wehrli, Matthew Hogancamp
I will discuss a deformation of the annular Khovanov homology that carries an action of the quantum sl(2). The first step is to construct an isomorphism between undeformed annular Khovanov homology and Hochschild hyperhomology of the Chen-Khovanov invariant of tangles, conjectured by Auroux, Grigsby, and Wehrli. Rephrasing this in the language of categorical traces allows us to recover the sl(2) action due to Grigsby, Licata, and Wehrli, and then deform it. The new invariant has many interesting properties. For instance, it assigns a nontrivial polynomials to knotted surfaces in S1 x D3 and the quantized colored Khovanov complex is homotopy equivalent to the Cooper–Krushal complex (so that both are finite dimensional).
This is a joint project with Anna Beliakova, Stephan Wehrli, and Matthew Hogancamp.
Date received: December 4, 2017
Copyright © 2017 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cboj-21.