Homology of framed links embedded in thickened surfaces

Details Homology of framed links embedded in thickened surfaces Homology of framed links embedded in thickened surfaces

2008-10-30

arxiv.org/abs/0810.5566v1

Mathematics

Geometric Topology

21 pages, 22 figures

Scientific paper

We construct an infinite family of homology theories of framed links in thickened surfaces, as well as a homology theory whose graded Euler characteristic is exactly the Kauffman bracket of the link in the surface. Both theories are based on ideas coming from Asaeda, Przytycki and Sikora's categorification of the Kauffman bracket skein module of I-bundles over surfaces. This is accomplished by borrowing ideas from Bar-Natan's Khovanov homology theory for tangles and cobordisms and using embedded surfaces to generate the chain groups, instead of diagrams.

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