Oberseminar Geometrie, Topologie und Analysis

H. Geiges, P. Konstantis, A. Lytchak, G. Marinescu

Wintersemester 2019/20

Freitag, 10:30-11:30, Seminarraum 2 (Raum 204)

11.10.19 BGHK Seminar in Köln

18.10.19 Fernando Galaz-García (KIT)
Smooth 2-torus actions on the 5-sphere

Abstract: Isometric torus actions on closed, simply-connected Riemannian manifolds with positive and non-negative sectional curvature have been extensively studied. In dimension 5, Rong proved that a closed, simply-connected Riemannian 5-manifold M with positive sectional curvature and an isometric action of the 2-torus must be diffeomorphic to the 5-sphere. In the case where M is assumed to have non-negative sectional curvature, Searle and I obtained a classification up to diffeomorphism of such manifolds. With these classification results in place, a next natural step is to classify all possible actions of the 2-torus on a given manifold. In this talk I will discuss the general equivariant classification of smooth 2-torus actions on the 5-sphere, as well as the equivariant classification of isometric 2-torus actions on a 5-sphere with a Riemannian metric with positive sectional curvature. This is joint work with Diego Corro and Martin Kerin.
25.10.19 BGHK Seminar in Heidelberg

15./16.11.19 Geometric Dynamics Days in Aachen

22.11.19 BGHK Seminar in Bochum

H. Geiges, 5.4.02