ON THE CHARACTER RINGS OF TWIST KNOTS

Title & Authors
ON THE CHARACTER RINGS OF TWIST KNOTS
Nagasato, Fumikazu;

Abstract
The Kauffman bracket skein module $\small{K_t}$(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 $\small{SL_2(\mathbb{C})}$-character ring of the fundamental group of M. Our proof is based on some properties of Chebyshev polynomials.
Keywords
character variety;character ring;Chebyshev polynomial;Kauffman bracket skein module;
Language
English
Cited by
1.
On minimal elements for a partial order of prime knots, Topology and its Applications, 2012, 159, 4, 1059
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