# ON THE CHARACTER RINGS OF TWIST KNOTS

• Published : 2011.05.31

#### Abstract

The Kauffman bracket skein module $K_t$(M) of a 3-manifold M becomes an algebra for t = -1. We prove that this algebra has no non-trivial nilpotent elements for M being the exterior of the twist knot in 3-sphere and, therefore, it is isomorphic to the $SL_2(\mathbb{C})$-character ring of the fundamental group of M. Our proof is based on some properties of Chebyshev polynomials.

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#### Cited by

1. On minimal elements for a partial order of prime knots vol.159, pp.4, 2012, https://doi.org/10.1016/j.topol.2011.11.022