Homology cylinders: an enlargement of the mapping class group
نویسنده
چکیده
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. AMS Classification 57N10; 57M25
منابع مشابه
Addendum and correction to: Homology cylinders: an enlargement of the mapping class group
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...
متن کامل2000]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...
متن کامل2000]Primary (57N10); Secondary (57M25). HOMOLOGY CYLINDERS: AN EXPANSION OF THE MAPPING CLASS GROUP
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 fi...
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