Meta-nilpotent knot invariants and symplectic automorphism groups of free nilpotent groups

TL;DR

This paper introduces a new class of knot invariants derived from automorphism groups of free nilpotent groups, using nilpotently p-localization, and explores their properties and computations.

Contribution

It develops nilpotently p-localized automorphism groups of free nilpotent groups to construct novel knot invariants and analyzes their automorphism groups.

Findings

Constructed new knot invariants from automorphism groups

Computed automorphism groups and resulting invariants

Established connections between knot invariants and symplectic automorphisms

Abstract

We develop nilpotently $p$-localization of knot groups in terms of the (symplectic) automorphism groups of free nilpotent groups. We show that any map from the set of conjugacy classes of the outer automorphism groups yields a knot invariant. We also investigate the automorphism groups and compute the resulting knot invariants.