Involutions on tori with codimension one fixed point set

TL;DR

This paper extends Smith theory to classify orientation-reversing involutions with codimension-one fixed points on tori, using topological surgery to achieve a complete topological classification in all dimensions.

Contribution

It introduces a comprehensive topological classification of involutions on tori with fixed points of codimension one, expanding Smith theory to new manifold types.

Findings

Complete topological classification of involutions on tori

Extension of Smith theory to product of circles

Application of surgery theory for classification

Abstract

The standard P. A. Smith theory of p-group actions on spheres, disks, and euclidean spaces is extended to the case of p-group actions on tori (i.e., products of circles) and coupled with topological surgery theory to give a complete topological classification, valid in all dimensions, of the locally linear, orientation reversing, involutions on tori with fixed point set of codimension one.