Mathematisches Kolloquium

Zusammenfassung: 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. I shall start by giving an overview of known results before presenting two different ways of how to take profit of group actions in this context. First, I shall illustrate how the existence of a torus action permits to determine the Euler characteristic, thus generalising a conjecture of Hopf in the presence of symmetry. Second, as a rather different transition from geometry to topology under symmetry, I shall discuss geometrically formal homogeneous metrics of positive curvature. Presented results come from joint work with Lee Kennard and Wolfgang Ziller, respectively.

Alle Interessierten sind hiermit herzlich eingeladen. Eine halbe Stunde vor dem Vortrag gibt es Kaffee und Tee im Sozialraum (Raum 448) im 4. Stock.

Treffpunkt zum Abendessen um 18.00 Uhr wird noch bekannt gegeben.