2000]Primary (57N10); Secondary (57M25). HOMOLOGY CYLINDERS: AN EXPANSION OF THE MAPPING CLASS GROUP
نویسنده
چکیده
We consider a homological expansion 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.
منابع مشابه
2000]Primary (57N10); Secondary (57M25). CORRECTION TO HOMOLOGY CYLINDERS: AN ENLARGEMENT OF THE MAPPING CLASS GROUP
In a previous paper [Le] math.GT/0010247 a group Hg of homology cylinders over the oriented surface of genus g is defined. A filtration of Hg is defined, using the Goussarov-Habiro notion of finite-type. It is erroneously claimed that this filtration essentially coincides with the relative weight filtration. The present note corrects this error and studies the actual relation between the two fi...
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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 ...
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In a previous paper [1], a group Hg of homology cylinders over the oriented surface of genus g is defined. A filtration of Hg is defined, using the Goussarov-Habiro notion of finite-type. It is erroneously claimed that this filtration essentially coincides with the relative weight filtration. The present note corrects this error and studies the actual relation between the two filtrations. AMS C...
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