Spectral sequences of colored Jones polynomials, colored Rasmussen invariants and nanophrases

Details Spectral sequences of colored Jones polynomials, colored Rasmussen invariants and nanophrases Spectral sequences of colored Jones polynomials, colored Rasmussen invariants and nanophrases

2010-08-26

arxiv.org/abs/1008.4443v2

Mathematics

Geometric Topology

8 pages. Second version: minor changes

Scientific paper

We introduce three spectral sequences which give some expressions of colored Jones polynomials. Each spectral sequence contains a Khovanov-type homology groups. Two of them are derived from a bicomplex of the colored Jones polynomial. The other is the spectral sequence that deduces a colored Rasmussen invariant of links. We also introduce three functors between categories of nanophrases, generalizations of links, and obtain their applications using colored Jones polynomials and their categorifications.

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