Volume 13, issue 5 (2013)

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Induced quasicocycles on groups with hyperbolically embedded subgroups

Michael Hull and Denis Osin

Algebraic & Geometric Topology 13 (2013) 2635–2665
Abstract

Let G be a group, H a hyperbolically embedded subgroup of G, V a normed G–module, U an H–invariant submodule of V . We propose a general construction which allows to extend 1–quasicocycles on H with values in U to 1–quasicocycles on G with values in V . As an application, we show that every group G with a nondegenerate hyperbolically embedded subgroup has dimHb2(G,p(G)) = for p 1. This covers many previously known results in a uniform way. Applying our extension to quasimorphisms and using Bavard duality, we also show that hyperbolically embedded subgroups are undistorted with respect to the stable commutator length.

Keywords
hyperbolic space, hyperbolically embedded subgroups, left regular representation, quasicocycle, bounded cohomology, stable commutator length
Mathematical Subject Classification 2010
Primary: 20F65, 20F67, 20J06, 43A15, 57M07
References
Publication
Received: 26 May 2012
Revised: 28 January 2013
Accepted: 9 February 2013
Published: 7 July 2013
Authors
Michael Hull
Department of Mathematics
Vanderbilt University
1326 Stevenson Center
Nashville, TN 37240
USA
http://math.vanderbilt.edu/people/hull
Denis Osin
Mathematics Department
Vanderbilt University
1326 Stevenson Center
Nashville, TN 37240
USA
http://math.vanderbilt.edu/people/osin