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Torsion in Khovanov Homology and links with smoothing number one
by
Xiao Wang
The George Washington University
Coauthors: Sujoy Mukherjee, Józef H. Przytycki, Marithania Silvero and Seung Yeop Yang

In the Khovanov homology of links, presence of Z₂-torsion is a very common phenomenon. Finite number of examples of knots with Z_n-torsion for n > 2 were also known, none for n > 8. In this talk, we demonstrate that there are infinite families of links with smoothing number one, whose Khovanov homology contains Z_n-torsion for 2 < n < 9 (T^k(n, n+2)) and Z_2^s-torsion for s < 24 (T^k(4, 4s+2)). The idea of the proof also works for other families, for instance T^k(n, n+1). We also provide an infinite family of links with Z₅-torsion in reduced Khovanov homology and Z₃-torsion in odd Khovanov homology. Finally, I will mention the possibility of computing the Khovanov homology of links with smoothing number one through Hochschild homology. This is a joint work with Mathathoners.

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-24.