Aspherical manifolds, relative hyperbolicity, simplicial volume and assembly maps

Details Aspherical manifolds, relative hyperbolicity, simplicial volume and assembly maps Aspherical manifolds, relative hyperbolicity, simplicial volume and assembly maps

2005-09-22

arxiv.org/abs/math/0509504v3

Algebr. Geom. Topol. 6 (2006) 1341-1354

Mathematics

Group Theory

This is the version published by Algebraic & Geometric Topology on 20 September 2006

Scientific paper

10.2140/agt.2006.6.1341

This paper contains examples of closed aspherical manifolds obtained as a by-product of recent work by the author [arXiv:math.GR/0509490] on the relative strict hyperbolization of polyhedra. The following is proved. (I) Any closed aspherical triangulated n-manifold M^n with hyperbolic fundamental group is a retract of a closed aspherical triangulated (n+1)-manifold N^(n+1) with hyperbolic fundamental group. (II) If B_1,...,B_m are closed aspherical triangulated n-manifolds, then there is a closed aspherical triangulated manifold N of dimension n+1 such that N has nonzero simplicial volume, N retracts to each B_k, and \pi_1(N) is hyperbolic relative to \pi_1(B_k)'s. (III) Any finite aspherical simplicial complex is a retract of a closed aspherical triangulated manifold with positive simplicial volume and non-elementary relatively hyperbolic fundamental group.

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