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Gluing Locally Symmetric Manifolds: Asphericity and Rigidity by Phan, T. Tam Nguyen is a scholarly article available to read on EtoBox.

What is Gluing Locally Symmetric Manifolds: Asphericity and Rigidity about?

We use the reflection group trick to glue manifolds with corners that are Borel-Serre compactifications of locally symmetric spaces of noncompact type and obtain aspherical manifolds. We call these \emph{piecewise locally symmetric} manifolds. This class of spaces provide new examples of aspherical manifolds whose fundamental groups have the structure of a complex of groups. These manifolds typically do not admit a locally $\CAT(0)$ metric. We prove that any self homotopy equivalence of such manifolds is homotopic to a homeomorphism. We compute the group of self homotopy equivalences of such a manifold and show that it can contain a normal free abelian subgroup, and thus can be infinite.

Author

Phan, T. Tam Nguyen

Published

2011

Language

EN