On Fixed-Point Sets of $\Z_2$-Tori in Positive Curvature
Differential Geometry
2024-11-04 v1 Algebraic Topology
Abstract
In recent work of Kennard, Khalili Samani, and the last author, they generalize the Half-Maximal Symmetry Rank result of Wilking for torus actions on positively curved manifolds to -tori with a fixed point. They show that if the rank is approximately one-fourth of the dimension of the manifold, then fixed point set components of small co-rank subgroups of the -torus are homotopy equivalent to spheres, real projective spaces, complex projective spaces, or lens spaces. In this paper, we lower the bound on the rank of the -torus to approximately and and are able to classify either the integral cohomology ring or the -cohomology ring, respectively, of the fixed point set of the -torus.
Keywords
Cite
@article{arxiv.2411.00665,
title = {On Fixed-Point Sets of $\Z_2$-Tori in Positive Curvature},
author = {Austin Bosgraaf and Christine Escher and Catherine Searle},
journal= {arXiv preprint arXiv:2411.00665},
year = {2024}
}