A volume form on the Khovanov invariant

Details A volume form on the Khovanov invariant A volume form on the Khovanov invariant

2008-11-30

arxiv.org/abs/0812.0151v1

Mathematics

Algebraic Topology

29 pages, 15 figures, 2 tables

Scientific paper

The Reidemeister torsion construction can be applied to the chain complex used to compute the Khovanov homology of a knot or a link. This defines a volume form on Khovanov homology. The volume form transforms correctly under Reidemeister moves to give an invariant volume on the Khovanov homology. In this paper, its construction and invariance under these moves is demonstrated. Also, some examples of the invariant are presented for particular choices for the bases of homology groups to obtain a numerical invariant of knots and links. In these examples, the algebraic torsion seen in the Khovanov chain complex when homology is computed over $\mathbb{Z}$ is recovered.

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