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('cloaka050a6c2856388d0a5b1a6f782539010').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addya050a6c2856388d0a5b1a6f782539010 = 'g&#111;r&#111;dsk&#105;' + '&#64;'; addya050a6c2856388d0a5b1a6f782539010 = addya050a6c2856388d0a5b1a6f782539010 + '&#105;m&#101;' + '&#46;' + '&#117;sp' + '&#46;' + 'br'; var addy_texta050a6c2856388d0a5b1a6f782539010 = 'g&#111;r&#111;dsk&#105;' + '&#64;' + '&#105;m&#101;' + '&#46;' + '&#117;sp' + '&#46;' + 'br';document.getElementById('cloaka050a6c2856388d0a5b1a6f782539010').innerHTML += '<a ' + path + '\'' + prefix + ':' + addya050a6c2856388d0a5b1a6f782539010 + '\'>'+addy_texta050a6c2856388d0a5b1a6f782539010+'<\/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).