On p-adic actions raising dimension by 2

TL;DR

This paper generalizes the construction of p-adic integer actions on compacta, showing that for any n>1, an (n+2)-dimensional orbit space can be obtained from an n-dimensional compactum if certain cohomological dimension conditions are met.

Contribution

It extends previous methods to characterize when (n+2)-dimensional orbit spaces arise from p-adic actions based on cohomological dimension constraints.

Findings

Characterization of orbit spaces via cohomological dimension.

Generalized construction method for p-adic actions.

Necessary and sufficient conditions for dimension raising.

Abstract

Raymond and Wiliams constructed an action of the p-adic integers on an n-dimensional compactum, n>1, with the orbit space of dimension n+2. The author earlier presented a simplified approach for constructing such an action. In this paper we generalize this approach to show that for every n>1, an (n+2)-dimensional compactum X can be obtained as the orbit space of an action of the p-adic integers on an n-dimensional compactum if and only if the cohomological dimension of X with coefficients in Z[1/p] is at most n.