Volume 11, issue 4 (2011)

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

Volume 24, 1 issue

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

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
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
Simplicial volume and fillings of hyperbolic manifolds

Koji Fujiwara and Jason Fox Manning

Algebraic & Geometric Topology 11 (2011) 2237–2264

Let M be a hyperbolic n–manifold whose cusps have torus cross-sections. In an earlier paper, the authors constructed a variety of nonpositively and negatively curved spaces as “2π–fillings” of M by replacing the cusps of M with compact “partial cones” of their boundaries. These 2π–fillings are closed pseudomanifolds, and so have a fundamental class. We show that the simplicial volume of any such 2π–filling is positive, and bounded above by Vol(M) vn , where vn is the volume of a regular ideal hyperbolic n–simplex. This result generalizes the fact that hyperbolic Dehn filling of a 3–manifold does not increase hyperbolic volume.

In particular, we obtain information about the simplicial volumes of some 4–dimensional homology spheres described by Ratcliffe and Tschantz, answering a question of Belegradek and establishing the existence of 4–dimensional homology spheres with positive simplicial volume.

simplicial volume, pseudomanifold, Dehn filling
Mathematical Subject Classification 2010
Primary: 20F65, 53C23
Received: 2 February 2011
Accepted: 3 June 2011
Published: 25 August 2011
Koji Fujiwara
Graduate School of Information Sciences
Tohoku University
Jason Fox Manning
Department of Mathematics
University at Buffalo, SUNY
Buffalo NY 14260