A note on the $\mathbb Z_2$-equivariant Montgomery-Yang correspondence

TL;DR

This paper classifies free involutions on 3-dimensional homotopy complex projective spaces and uses the $Z_2$-equivariant Montgomery-Yang correspondence to identify all smooth involutions on $S^6$ with fixed-point set an embedded $S^3$.

Contribution

It provides a classification of free involutions on certain 3-manifolds and applies a specialized correspondence to determine involutions on $S^6$ with specific fixed points.

Findings

Classified free involutions on 3-dimensional homotopy complex projective spaces.

Identified all smooth involutions on $S^6$ with fixed-point set an embedded $S^3$.

Applied $Z_2$-equivariant Montgomery-Yang correspondence to achieve these results.

Abstract

In this paper, a classification of free involutions on 3-dimensional homotopy complex projective spaces is given. By the $\mathbb Z_2$-equivariant Montgomery-Yang correspondence, we obtain all smooth involutions on $S^6$ with fixed-point set an embedded $S^3$.