Lecture Event
Weitzenböckformeln auf Mannigfaltigkeiten mit spezieller Holonomie
Prof. Dr. Uwe Semmelmann
21 Jan 2009, 17:00 – 18:30
Weitzenboeck formulas are an important tool for linking differential geometry
and topology. They may be used for proving the vanishing of Betti numbers
under suitable curvature assumptions or for proving the non existence of
metrics of positive scalar curvature on manifolds satisfying certain topological
conditions. Moreover they are often applied in the proof of eigenvalue
estimates for Laplace and Dirac operators.
In my talk I will consider Weitzenboeck formulas on Riemannian manifolds
with a fixed compact structure group. I will show how one may derive all
such formulas in a certain recursive procedure. It turns out that finding all
possible Weitzenboeck formulas can be reformulated into a problem of linear
algebra depending on the representation theory of the structure group. In
the end the structure of the universal enveloping algebra of the Lie algebra
of the structure group determines the existence of Weitzenboeck formulas.
Forschungsseminar Geometrie: http://users.math.uni-potsdam.de/%7Epfaeffle/oberseminar/ws2008.html
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