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2006 Aspherical manifolds, relative hyperbolicity, simplicial volume and assembly maps
Igor Belegradek
Algebr. Geom. Topol. 6(3): 1341-1354 (2006). DOI: 10.2140/agt.2006.6.1341

Abstract

This paper contains examples of closed aspherical manifolds obtained as a by-product of recent work by the author [?] on the relative strict hyperbolization of polyhedra. The following is proved.

(I) Any closed aspherical triangulated n–manifold Mn with hyperbolic fundamental group is a retract of a closed aspherical triangulated (n+1)–manifold Nn+1 with hyperbolic fundamental group.

(II) If B1,Bm 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 Bk, and π1(N) is hyperbolic relative to π1(Bk)’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.

Citation

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Igor Belegradek. "Aspherical manifolds, relative hyperbolicity, simplicial volume and assembly maps." Algebr. Geom. Topol. 6 (3) 1341 - 1354, 2006. https://doi.org/10.2140/agt.2006.6.1341

Information

Received: 19 October 2005; Accepted: 30 June 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1137.20035
MathSciNet: MR2253450
Digital Object Identifier: 10.2140/agt.2006.6.1341

Subjects:
Primary: 20F65

Rights: Copyright © 2006 Mathematical Sciences Publishers

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