Volume 6, issue 2 (2006)

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
Homology cylinders and the acyclic closure of a free group

Takuya Sakasai

Algebraic & Geometric Topology 6 (2006) 603–631

arXiv: math.GT/0507260

Abstract

We give a Dehn–Nielsen type theorem for the homology cobordism group of homology cylinders by considering its action on the acyclic closure, which was defined by Levine, of a free group. Then we construct an additive invariant of those homology cylinders which act on the acyclic closure trivially. We also describe some tools to study the automorphism group of the acyclic closure of a free group generalizing those for the automorphism group of a free group or the homology cobordism group of homology cylinders.

Keywords
homology cylinder, acyclic closure, mapping class group
Mathematical Subject Classification 2000
Primary: 20F28
Secondary: 20F34, 57M05, 57M27
References
Forward citations
Publication
Received: 13 October 2005
Revised: 10 February 2006
Accepted: 23 March 2006
Published: 7 April 2006
Authors
Takuya Sakasai
Graduate School of Mathematical Sciences
the University of Tokyo
3-8-1 Komaba
Meguro-ku
Tokyo 153-8914
Japan