2 jul 2015 -- 16:30
Bielefeld University
Abstract.
Manifolds admitting metrics of positive sectional curvature are conjectured to have a very rigid topological structure. However, this structure is still highly speculative and the strongest results in this direction are known under the assumption of Lie group actions. In this talk I shall try to illustrate this interplay between geometry, symmetry and topology. In particular, using such symmetry assumptions, I will speak about generalisations of a conjecture by Hopf which states that $\mathbb{S}^2×\mathbb{S}^2$ cannot carry a metric of positive curvature. Presented results come from joint work with Lee Kennard.