## View abstract

### Session S23 - Group actions in Differential Geometry

Friday, July 23, 17:20 ~ 17:50 UTC-3

## A diameter gap for isometric quotients of the unit sphere

### Claudio Gorodski

#### University of São Paulo, Department of Mathematics, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak0fffc6119ee2d53b35261273f3ea1161').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy0fffc6119ee2d53b35261273f3ea1161 = 'g&#111;r&#111;dsk&#105;' + '&#64;'; addy0fffc6119ee2d53b35261273f3ea1161 = addy0fffc6119ee2d53b35261273f3ea1161 + '&#105;m&#101;' + '&#46;' + '&#117;sp' + '&#46;' + 'br'; var addy_text0fffc6119ee2d53b35261273f3ea1161 = 'g&#111;r&#111;dsk&#105;' + '&#64;' + '&#105;m&#101;' + '&#46;' + '&#117;sp' + '&#46;' + 'br';document.getElementById('cloak0fffc6119ee2d53b35261273f3ea1161').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy0fffc6119ee2d53b35261273f3ea1161 + '\'>'+addy_text0fffc6119ee2d53b35261273f3ea1161+'<\/a>';

We will explain our proof of the existence of $\epsilon>0$ such that every quotient of the unit sphere $S^n$ ($n\geq2$) by an isometric group action has diameter zero or at least $\epsilon$. The novelty is the independence of $\epsilon$ from $n$. The classification of finite simple groups is used in the proof.

Joint work with Christian Lange (University of Cologne, Germany), Alexander Lytchak (University of Cologne, Germany) and Ricardo A. E. Mendes (University of Oklahoma, USA).