On tangle decompositions of twisted torus knots
Kanji Morimoto
TL;DR
This paper demonstrates that for any positive integer n, there exist infinitely many twisted torus knots that admit n-string essential tangle decompositions, expanding understanding of knot decomposition structures.
Contribution
It establishes the existence of infinitely many twisted torus knots with specified tangle decomposition properties for any number of strings.
Findings
Existence of infinitely many such knots for each n>0
Construction methods for these knots
Implications for knot decomposition theory
Abstract
In the present paper, we will show that for any integer n>0 there are infinitely many twisted torus knots with n-string essential tangle decompositions.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models