On Reidemeister invariance of the Khovanov homology group of the Jones polynomial

Details On Reidemeister invariance of the Khovanov homology group of the Jones polynomial On Reidemeister invariance of the Khovanov homology group of the Jones polynomial

2009-01-26

arxiv.org/abs/0901.3952v4

Mathematics

Geometric Topology

6 pages. Typos in mappings were corrected, Revised the title

Scientific paper

As Oleg Viro describes in his paper, the most fundamental property of the Khovanov homology group is their invariance under Reidemeister moves. Viro constructes Khovanov complex and homology consisting of Jordan curves with sign and also gives a proof for the only case of first Reidemeister move by using his definition of Khovanov homology groups. In this paper, homotopy maps are obtained explicitly for the other Reidemeister moves, i.e. second and third.

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