Profinite rigidity for two-bridge links and 3-tangle Montesinos links

TL;DR

This paper proves that the fundamental groups of two-bridge links and 3-tangle Montesinos links are uniquely determined by their profinite completions, establishing a form of algebraic rigidity in 3-manifold topology.

Contribution

It establishes profinite rigidity for a broad class of links, including all two-bridge and 3-tangle Montesinos links, among fundamental groups of compact orientable 3-manifolds.

Findings

Profinite completions uniquely determine the fundamental groups of these links.

The result applies to all two-bridge links and 3-tangle Montesinos links, including knots.

It advances understanding of algebraic invariants in 3-manifold topology.

Abstract

For any two-bridge link or 3-tangle Montesinos link $L\subset S^3$ (including knot), this paper proves that $\pi_1(S^3-L)$ is profinitely rigid among the fundamental groups of compact orientable 3-manifolds.