## View abstract

### Session S23 - Group actions in Differential Geometry

Friday, July 23, 19:40 ~ 20:10 UTC-3

## Torus actions on Alexandrov $4$-spaces

### Jesús Núñez-Zimbrón

#### CIMAT, Mexico   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak4efd74696415e0da6cac8ffe4590f84d').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy4efd74696415e0da6cac8ffe4590f84d = 'j&#101;s&#117;s.n&#117;n&#101;z' + '&#64;'; addy4efd74696415e0da6cac8ffe4590f84d = addy4efd74696415e0da6cac8ffe4590f84d + 'c&#105;m&#97;t' + '&#46;' + 'mx'; var addy_text4efd74696415e0da6cac8ffe4590f84d = 'j&#101;s&#117;s.n&#117;n&#101;z' + '&#64;' + 'c&#105;m&#97;t' + '&#46;' + 'mx';document.getElementById('cloak4efd74696415e0da6cac8ffe4590f84d').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy4efd74696415e0da6cac8ffe4590f84d + '\'>'+addy_text4efd74696415e0da6cac8ffe4590f84d+'<\/a>';

Alexandrov spaces are metric spaces which are not necessarily smooth but admit a notion of "sectional curvature bounded below". In contrast to manifolds, these spaces may have topological or metric singularities. Nevertheless, many typical results from Riemannian geometry hold in this more general setting. In this talk I will speak about an equivariant classification and a partial topological classification of torus actions on orientable Alexandrov spaces of dimension four, generalizing previous work of Orlik and Raymond originally obtained in the case of four-dimensional manifolds.

Joint work with Diego Corro (Universidad Nacional Autónoma de México) and Masoumeh Zarei (University of Augsburg).