4.5 Article

STABILIZATION FOR MAPPING CLASS GROUPS OF 3-MANIFOLDS

Journal

DUKE MATHEMATICAL JOURNAL
Volume 155, Issue 2, Pages 205-269

Publisher

DUKE UNIV PRESS
DOI: 10.1215/00127094-2010-055

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Funding

  1. National Science Foundation [DMS-05044932]
  2. Mittag-Leffler Institute
  3. Danish Natural Science Research Council

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We prove that the homology of the mapping class group of any 3-manifold stabilizes under connected stun and boundary connected sum with an arbitrary 3-manifold when both manifolds are compact and orientable. The stabilization also holds for the quotient group by twists along spheres and disks and includes as particular cases homological stability for symmetric automorphisms of free groups, automorphisms of certain free products, and handlebody mapping class groups. Our methods also apply to manifolds of other dimensions in the case of stabilization by punctures.

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