On the degeneration ratio of tunnel numbers and free tangle decompositions of knots

TL;DR

This paper introduces the concept of n/k-free tangles to analyze how tunnel numbers of knots change under certain decompositions, providing insights into knot complexity reduction.

Contribution

It presents a new notion called n/k-free tangle and investigates its impact on the degeneration ratio of knot tunnel numbers.

Findings

Defined n/k-free tangle concept

Analyzed degeneration ratio of tunnel numbers

Provided theoretical insights into knot decompositions

Abstract

In this paper, we introduce a notion called n/k-free tangle and study the degeneration ratio of tunnel numbers of knots.