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Torsion of the Khovanov Homology
by
Alexander Shumakovitch
Dartmouth College
Given a diagram D of an oriented link L in the 3-sphere, one can assign to it a family of Abelian groups Hi, j(D) using a construction due to Mikhail Khovanov. These groups are defined as homology groups of an appropriate (graded) chain complex C(D), and their isomorphism classes depend on the isotopy class of L only. The graded Euler characteristic of C(D) is a version of the Jones polynomial of L.
Although the ranks of the Khovanov homology groups have many remarkable properties, their torsion appear to be even more fascinating. In this talk, we prove several properties of this torsion, discuss methods of its calculation and finally formulate several conjectures about it.
Date received: December 10, 2003
Copyright © 2003 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 # camw-15.