Z_p-Torus Actions and Positive Curvature, Catherine Searle (Wichita State University)

Iscrizioni 25-26

Abstract: Using work of Fang and Rong in even dimensions and of Ghazawneh in odd dimensions one can show that closed, positively curved manifolds admitting an isometric and effective $\Z_p^r$-action with a fixed point with $r$ greater than approximately $3n/8$, the manifold is homotopy equivalent to $S^n$, $\mathbb{R}\mathrm{P}^n$, $\mathbb{C}\mathrm{P}^{n/2}$ or a lens space. In this talk, I'll discuss how we can lower the bound on $r$ for all odd primes $p$, and obtain the same classification. The result involves the use of error correcting code techniques, as well as recent algebraic topological tools developed by Kennard, Khalili Samani, and Searle.

Relatori/Relatrici

Prof.ssa Catherine Searle

Full Professor in the Department of Mathematics, Statistics, and Physics at Wichita State University, she works in Differential Geometry with an emphasis on Comparison Geometry. Her research has been focussed on positively and non-negatively curved Riemannian manifolds, which admit “large” isometric group actions, where “large” can be defined in a number of ways. The existence of an isometric group action G on a metric space X leads to information about the space itself and can be used both as a tool to identify the space and as a means to improve the metric on that space. More recently she has been studying isometric group actions in these two contexts, namely, as a tool to identify both Riemannian manifolds and Alexandrov spaces with a lower curvature bound and as a tool to improve the metric on a Riemannian manifold with a G-invariant metric.

https://sites.google.com/site/catherinesearle1/home