Volume 19, issue 6 (2015)

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

Volume 28
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
The stable homology of congruence subgroups

Frank Calegari

Geometry & Topology 19 (2015) 3149–3191
Abstract

We relate the completed cohomology groups of SLN(OF), where OF is the ring of integers of a number field, to K–theory and Galois cohomology. Various consequences include showing that Borel’s stable classes become infinitely p–divisible up the p–congruence tower if and only if a certain p–adic zeta value is nonzero. We use our results to compute H2(ΓN(p), Fp) (for sufficiently large N), where ΓN(p) is the full level-p congruence subgroup of SLN().

Keywords
arithmetic groups, stable homology, completed homology, $K$–theory
Mathematical Subject Classification 2010
Primary: 11F75, 19F99
Secondary: 11F80
References
Publication
Received: 7 November 2013
Revised: 27 December 2014
Accepted: 26 January 2015
Published: 6 January 2016
Proposed: Benson Farb
Seconded: Danny Calegari, Walter Neumann
Authors
Frank Calegari
Department of Mathematics
Northwestern University
2033 Sheridan Road
Evanston, IL 60208
USA