Download or read book Gluing Locally Symmetric Manifolds: Asphericity and Rigidity written by Tu Tam Nguyen Phan and published by . This book was released on 2012 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 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 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 there are examples in which this group is infinite.