Homotopical Intersection Theory, II: equivariance

TL;DR

This paper develops a homotopy theoretic intersection theory for manifolds with finite group actions, addressing embedding, fixed point, and periodic point problems without relying on equivariant transversality.

Contribution

It introduces a novel homotopy theoretic framework for equivariant intersection theory, extending previous work to include finite group actions.

Findings

Provides a new approach to equivariant intersection problems

Applications to fixed point and periodic point enumeration

Circumvents the need for equivariant transversality

Abstract

This is the second in a series of papers. Here we develop here an intersection theory for manifolds equipped with an action of a finite group. As in our previous paper, our approach will be homotopy theoretic, enabling us to circumvent the specter of equivariant transversality. This theory has applications to embedding problems, equivariant fixed point theory and the problem of enumerating the periodic points of a self map of a compact smooth manifold.