Deciding almost freeness of an action is NP-hard

TL;DR

This paper proves that determining whether a compact Lie group action on a manifold is almost free is an NP-hard problem, using Sullivan models to encode the actions.

Contribution

It introduces a novel NP-hardness result for the almost freeness decision problem of Lie group actions via Sullivan models.

Findings

Deciding almost freeness is NP-hard.

Uses Sullivan models to encode group actions.

Provides complexity results in geometric topology.

Abstract

We encode a compact Lie group action on a compact manifold by the Sullivan model of its Borel construction. We then prove that deciding whether this action is almost free is NP-hard.