Volume 14, issue 3 (2014)

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

Volume 20
Issue 7, 3219–3760
Issue 6, 2687–3218
Issue 5, 2145–2685
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

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
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Rational homological stability for groups of partially symmetric automorphisms of free groups

Matthew C B Zaremsky

Algebraic & Geometric Topology 14 (2014) 1845–1879
Abstract

Let Fn+m be the free group of rank n + m, with generators x1,,xn+m. An automorphism ϕ of Fn+m is called partially symmetric if for each 1 i m, ϕ(xi) is conjugate to xj or xj1 for some 1 j m. Let ΣAutnm be the group of partially symmetric automorphisms. We prove that for any m 0 the inclusion ΣAutnm ΣAutn+1m induces an isomorphism in rational homology for dimensions i satisfying n (3(i + 1) + m)2, with a similar statement for the groups PΣAutnm of pure partially symmetric automorphisms. We also prove that for any n 0 the inclusion ΣAutnm ΣAutnm+1 induces an isomorphism in rational homology for dimensions i satisfying m > (3i 1)2.

Keywords
partially symmetric automorphism, homological stability
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 20F28, 57M07
References
Publication
Received: 17 January 2013
Revised: 21 October 2013
Accepted: 15 November 2013
Published: 29 May 2014
Authors
Matthew C B Zaremsky
Department of Mathematical Sciences
Binghamton University
Binghamton, NY 13902
USA
http://www.math.binghamton.edu/zaremsky/