Open Access
Translator Disclaimer
2006 Homology cylinders and the acyclic closure of a free group
Takuya Sakasai
Algebr. Geom. Topol. 6(2): 603-631 (2006). DOI: 10.2140/agt.2006.6.603

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.

Citation

Download Citation

Takuya Sakasai. "Homology cylinders and the acyclic closure of a free group." Algebr. Geom. Topol. 6 (2) 603 - 631, 2006. https://doi.org/10.2140/agt.2006.6.603

Information

Received: 13 October 2005; Revised: 10 February 2006; Accepted: 23 March 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1149.57001
MathSciNet: MR2220691
Digital Object Identifier: 10.2140/agt.2006.6.603

Subjects:
Primary: 20F28
Secondary: 20F34, 57M05, 57M27

Rights: Copyright © 2006 Mathematical Sciences Publishers

JOURNAL ARTICLE
29 PAGES


SHARE
Vol.6 • No. 2 • 2006
MSP
Back to Top