Nonabelian representations and signatures of double twist knots

TL;DR

This paper verifies Riley's conjecture linking real parabolic representations to signatures of double twist knots, advancing understanding of knot invariants and their algebraic representations.

Contribution

It confirms Riley's conjecture for a class of double twist knots, establishing a connection between representations and signatures.

Findings

Riley's conjecture holds for double twist knots

Established a link between real parabolic representations and signatures

Enhanced understanding of knot invariants in algebraic topology

Abstract

A conjecture of Riley about the relationship between real parabolic representations and signatures of two-bridge knots is verified for double twist knots.