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Hyperbolic L-space knots and their formal semigroups

Department of Mathematic Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-hiroshima 7398524, Japan

E-mail Address: teragai@hiroshima-u.ac.jp

https://doi.org/10.1142/S0129167X2250080XCited by:2 (Source: Crossref)

Abstract

For an L-space knot, the formal semigroup is defined from its Alexander polynomial. It is not necessarily a semigroup. That is, it may not be closed under addition. There exists an infinite family of hyperbolic L-space knots whose formal semigroups are semigroups generated by three elements. In this paper, we give the first infinite family of hyperbolic L-space knots whose formal semigroups are semigroups generated by five elements.

Communicated by Jongil Park

Keywords:

AMSC: 57K10

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