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QGM seminar by Hao Guo (University of Adelaide)

Title: Positive Scalar Curvature for Proper Actions

2018.01.19 | Christine Dilling

Date Fri 19 Jan
Time 13:15 14:15
Location G1 (1532-116)

Let G be a Lie group acting properly on a G-Spin manifold M. In this talk I will explain recent work, joint with Mathai Varghese and Hang Wang, on certain obstructions to, and existence of, G-invariant metrics of positive scalar curvature on M. The principal obstruction we obtain comes by proving a vanishing theorem in equivariant index theory, giving as a corollary a recent result of Weiping Zhang. Existence of G-invariant metrics of positive scalar curvature is established under certain general hypotheses on the G-action on M, and makes use of a result of Vilms adapted to the equivariant setting, together with a theorem of Lawson and Yau.