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Abstract
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The set of homology cobordisms from a surface to itself with markings of their
boundaries has a natural monoid structure. To investigate the structure of this
monoid, we define and study its Magnus representation and Reidemeister torsion
invariants by generalizing Kirk, Livingston and Wang’s argument over the Gassner
representation of string links. Then, by applying Cochran and Harvey’s framework of
higher-order (noncommutative) Alexander invariants to them, we extract several
information about the monoid and related objects.
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Keywords
homology cylinder, Magnus representation, higher-order
Alexander invariant, string link, Reidemeister torsion,
Dieudonné determinant
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Mathematical Subject Classification 2000
Primary: 57M05
Secondary: 57M27, 20F34, 57N05
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Publication
Received: 30 November 2006
Accepted: 23 January 2008
Published: 3 June 2008
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