Riley's Conjecture on SL(2,R) Representations of 2-Bridge Knots

TL;DR

This paper proves Riley's conjecture regarding the count of parabolic SL(2,R) representations for 2-bridge knot groups, advancing understanding of their algebraic structure.

Contribution

The paper confirms Riley's conjecture, providing a definitive count of parabolic SL(2,R) representations for 2-bridge knots, which was previously unresolved.

Findings

Confirmed Riley's conjecture on the number of representations

Established a new link between knot theory and SL(2,R) representations

Enhanced understanding of 2-bridge knot group structures

Abstract

We prove Riley's conjecture on the number of parabolic SL(2,R) representations of 2-bridge knot groups.