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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-2-8,
author = {Allan L. Edmonds},
title = {Involutions on tori with codimension-one fixed point set},
journal = {Colloquium Mathematicae},
volume = {116},
year = {2009},
pages = {257-266},
zbl = {1198.57021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-2-8}
}
Allan L. Edmonds. Involutions on tori with codimension-one fixed point set. Colloquium Mathematicae, Tome 116 (2009) pp. 257-266. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-2-8/