Homfly polynomials for periodic knots via state model
Joonoh Kim, Kyoung-Tark Kim
TL;DR
This paper develops criteria using quantum invariants to determine if an oriented link is periodic of prime order, focusing on linking numbers and symmetry properties.
Contribution
It introduces new criteria based on quantum SL(N) invariants and linking numbers to identify periodicity in knots and links.
Findings
Criteria for periodicity based on quantum invariants.
Linking number analysis for detecting symmetry.
Application to prime order periodic knots.
Abstract
We give criteria for oriented links to be periodic of prime order using the quantum -invariant. The criteria are based upon an observation on the linking number between a periodic knot and its axis of the rotation.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Algebraic structures and combinatorial models