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arXiv · 1907.00569

On knot semigroups and Gelfand-Kirillov dimensions

Toshinori Miyatani
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Abstract

A knot semigroup is defined by A. Vernitski. A. Vernitski conjectured that the knot semigroup of the 2-bridge knot is isomorphic to an alternating sum semigroup. To support this conjecture, and as a first main result, we prove that the knot semigroup of the double twist knot is isomorphic to an alternating sum semigroup. Moreover, as a second main result, we construct a link invariant constructed by the Gelfand-Kiriliov dimension of algebra.

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Toshinori Miyatani. 2019-11-28. On knot semigroups and Gelfand-Kirillov dimensions. https://arxiv.org/abs/1907.00569

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