Positive curvature and discrete abelian symmetry

TL;DR

This paper extends known symmetry results for positively curved manifolds by replacing the torus with an elementary abelian two-group, broadening the class of symmetric spaces studied.

Contribution

It generalizes the maximal and half-maximal symmetry results to manifolds with elementary abelian two-group actions instead of torus actions.

Findings

Generalization of symmetry results to elementary abelian two-groups

Broader class of positively curved manifolds with symmetry

New insights into manifold symmetry structures

Abstract

By replacing the torus with an elementary abelian two-group, we generalize the maximal symmetry result of Grove and Searle and the half-maximal symmetry result of Wilking for positively curved manifolds with an isometric torus action.