On knot semigroups and Gelfand-Kirillov dimensions
Combinatorics
2019-12-02 v3 Algebraic Topology
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.
Cite
@article{arxiv.1907.00569,
title = {On knot semigroups and Gelfand-Kirillov dimensions},
author = {Toshinori Miyatani},
journal= {arXiv preprint arXiv:1907.00569},
year = {2019}
}
Comments
22 pages, 15 figures