Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial

Details Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial

2011-06-20

arxiv.org/abs/1106.3948v1

Mathematics

Geometric Topology

27 pages

Scientific paper

We study the head and tail of the colored Jones polynomial while focusing mainly on alternating links. Various ways to compute the colored Jones polynomial for a given link give rise to combinatorial identities for those power series. We further show that the head and tail functions only depend on the reduced checkerboard graphs of the knot diagram. Moreover the class of head and tail functions of prime alternating links forms a monoid.

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