Volume 6, issue 3 (2006)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Aspherical manifolds, relative hyperbolicity, simplicial volume and assembly maps

Igor Belegradek

Algebraic & Geometric Topology 6 (2006) 1341–1354

arXiv: math.GR/0509504


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.

hyperbolic, relatively hyperbolic, hyperbolization of polyhedra, aspherical manifold, simplicial volume, assembly map, Novikov Conjecture
Mathematical Subject Classification 2000
Primary: 20F65
Forward citations
Received: 19 October 2005
Accepted: 30 June 2006
Published: 20 September 2006
Igor Belegradek
School of Mathematics
Georgia Institute of Technology
Atlanta GA 30332–0160