Strongly invertible knots, invariant surfaces, and the Atiyah-Singer signature theorem

TL;DR

This paper introduces a new invariant for strongly invertible knots using the G-signature theorem, linking knot theory with the Atiyah-Singer signature theorem to deepen understanding of knot symmetries.

Contribution

It defines a novel invariant for strongly invertible knots based on the G-signature theorem, expanding the toolkit for knot classification.

Findings

New invariant for strongly invertible knots introduced

Connections established between knot invariants and the Atiyah-Singer theorem

Potential applications in knot symmetry analysis

Abstract

We use the G-signature theorem to define an invariant of strongly invertible knots analogous to the knot signature.