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Abstract
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We consider a homological enlargement of the mapping class group, defined by
homology cylinders over a closed oriented surface (up to homology cobordism).
These are important model objects in the recent Goussarov–Habiro theory of
finite-type invariants of 3–manifolds. We study the structure of this group
from several directions: the relative weight filtration of Dennis Johnson, the
finite-type filtration of Goussarov–Habiro, and the relation to string link
concordance.
We also consider a new Lagrangian filtration of both the mapping class group and
the group of homology cylinders.
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Keywords
homology cylinder, mapping class group, clasper,
finite-type invariant
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Mathematical Subject Classification 2000
Primary: 57N10
Secondary: 57M25
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Publication
Received: 14 November 2000
Accepted: 17 April 2001
Published: 23 April 2001
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