Translator Disclaimer
2016 The $L^2$–(co)homology of groups with hierarchies
Boris Okun, Kevin Schreve
Algebr. Geom. Topol. 16(5): 2549-2569 (2016). DOI: 10.2140/agt.2016.16.2549

Abstract

We study group actions on manifolds that admit hierarchies, which generalizes the idea of Haken n–manifolds introduced by Foozwell and Rubinstein. We show that these manifolds satisfy the Singer conjecture in dimensions n 4. Our main application is to Coxeter groups whose Davis complexes are manifolds; we show that the natural action of these groups on the Davis complex has a hierarchy. Our second result is that the Singer conjecture is equivalent to the cocompact action dimension conjecture, which is a statement about all groups, not just fundamental groups of closed aspherical manifolds.

Citation

Download Citation

Boris Okun. Kevin Schreve. "The $L^2$–(co)homology of groups with hierarchies." Algebr. Geom. Topol. 16 (5) 2549 - 2569, 2016. https://doi.org/10.2140/agt.2016.16.2549

Information

Received: 5 July 2014; Revised: 24 September 2015; Accepted: 6 April 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1383.20028
MathSciNet: MR3572340
Digital Object Identifier: 10.2140/agt.2016.16.2549

Subjects:
Primary: 20F65
Secondary: 20J05

Rights: Copyright © 2016 Mathematical Sciences Publishers

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.16 • No. 5 • 2016
MSP
Back to Top