2011/08/20 by T. Tam Nguyen Phan, Phan, T. Tam Nguyen · 1 citation
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT
paper · pdf · doi:10.48550/arxiv.1108.4127
26 pages, 2 figures
arxiv created 2011/08/20 · arxiv updated 2011/08/23
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 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.