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Torsion in the Khovanov Homology of Closed 3-Braids
by
Victor Summers
North Carolina State University
Coauthors: Alex Chandler, Adam Lowrance, Radmila Sazdanovic
Integral Khovanov homology is a bigraded homology theory for links in the 3-sphere.
These homology groups may contain torsion subgroups, and efforts have been made
to identify different types of torsion occurring in Khovanov homology for various classes
of knots and links. For example, in 2004 A. Shumakovitch showed that only Z/2-torsion
can appear in the Khovanov homology of non-split alternating links. In this talk I will
use a classification of 3-braids due to Kunio Murasugi, in conjunction with the skein
long exact sequence, to demonstrate that no odd torsion occurs in the Khovanov
homology of closed 3-braids.
Date received: April 30, 2018
Copyright © 2018 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 # cboy-38.