Mostow rigidity part I
Connections for Women: Geometric Group Theory
August 23, 2007 09:00 AM to 09:50 AM
Speakers:
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Abstract: |
A common theme in geometric group theory is to understand when complicated geometric structures are determined by simpler data. Thus, we are looking for rigidity phenomena. An important rigidity theorem which until today motivates a lot of research is Mostow's Rigidity theorem, which states that sometimes a manifold is completely determined by its fundamental group.
Namely, let M and N be non-positively curved locally symmetric manifolds
and assume that no factor of M or N is a surface or a torus. Then, if the
manifolds M and N have isomorphic fundamental groups they are actually isometric. This is quite amazing as
it implies for example that the volumeof such manifolds is a topological invariant.
In this minicourse we will discuss and prove Mostow's Rigidity Theorem in the special case when M and N are
hyperbolic manifolds. The proof is based on methods developed by Besson-Courtois-Gallot which lead to several new rigidity results within the last ten years. |
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Lecture #12527
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