Involutions onS6with 3–dimensional fixed point set

Involutions on Tori with Codimension-one Fixed Point Set

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.

Fixed point free involutions on Riemann surfaces

Involutions without fixed points on hyperbolic closed Riemann surface are discussed. Notably, the following question is answered: for τ such an involution on a surface (S, d), can a point p be chosen so that d(p, τ(p)) is bounded by a constant dependent solely on the genus of S? This is proved to be true for even genus and false otherwise. Furthermore, the sharp constant is given in genus 2.

Fixed Point Shifts of Inert Involutions

Given a mixing shift of finite type X , we consider which subshifts of finite type Y ⊂ X can be realized as the fixed point shift of an inert involution of X . We establish a condition on the periodic points of X and Y that is necessary for Y to be the fixed point shift of an inert involution of X . We show that this condition is sufficient to realize Y as the fixed point shift of an involution...

Fixed Point Free Involutions and Equivariant Maps

1. Preliminaries. We are concerned with involutions without fixed points, together with equivariant maps connecting such involutions. An involution T is a homeomorphism of period 2 of a Hausdorff space X onto itself; that is, T(x) = x for all x £ X . There is associated with an involution T on X the orbit space X/T, obtained by identifying x with T(x) for all x G Z . Denote by v\ X—+X/T the dec...

Fixed Point Sets of Involutions on Spheres