Homology cylinders and the acyclic closure of a free group

Sakasai, Takuya

doi:10.2140/agt.2006.6.603

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Homology cylinders and the acyclic closure of a free group

Takuya Sakasai

Algebraic & Geometric Topology 6 (2006) 603–631

DOI: 10.2140/agt.2006.6.603

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

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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

Volume 6, issue 2 (2006)