Geodesic
Homology cylinders and the acyclic closure of a free group
Sakasai, Takuya1
1Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
Algebraic and Geometric Topology, Tome 6 (2006) no. 2, pp. 603-631
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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.

DOI : 10.2140/agt.2006.6.603
Keywords: homology cylinder, acyclic closure, mapping class group

Sakasai, Takuya  1

1 Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan 
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Sakasai, Takuya. Homology cylinders and the acyclic closure of a free group. Algebraic and Geometric Topology, Tome 6 (2006) no. 2, pp. 603-631. doi: 10.2140/agt.2006.6.603

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