Stabilization for mapping class groups of 3-manifolds
Allen Hatcher,Nathalie Wahl +1 more
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TLDR
In this paper, the homology of the mapping class group of any 3-manifold stabilizes under connected sum and boundary connected sum with an arbitrary 3-Manifold when both manifolds are compact and orientable.Abstract:
We prove that the homology of the mapping class group of any 3-manifold stabilizes under connected sum 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.read more
Citations
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Homological stability for moduli spaces of high dimensional manifolds
TL;DR: In this article, the Madsen-Weiss theorem for moduli spaces of manifolds of dimension 2n was shown to hold for any simply-connected manifold of dimension at least 6.
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Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields
TL;DR: In this article, a homological stabilization theorem for Hurwitz spaces has been proved for moduli spaces of branched covers of the complex projective line, where the moduli space is moduli set of a set of moduli of the modulus space.
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Homological stability for automorphism groups
TL;DR: In this paper, a family of groups admitting a braided monoidal structure is constructed, and the authors show that homological stability holds with both polynomial and abelian twisted coefficients, with no further assumptions.
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Representation stability and finite linear groups
Andrew Putman,Steven V Sam +1 more
TL;DR: In this paper, the role of the symmetric group is played by the general linear groups and the symplectic groups over finite rings and prove basic structural properties such as Noetherianity.
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Homological stability for the mapping class groups of non-orientable surfaces
TL;DR: In this paper, it was shown that the stable rational cohomology of non-orientable surfaces is a polynomial algebra on generators in degrees 4i, which is the non-oriented analogue of the Mumford conjecture.
References
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Book
Cohomology of Groups
TL;DR: In this paper, an advanced textbook introduces students to cohomology theory and no knowledge of homological algebra is assumed beyond what is normally taught in a first course in algebraic topology.
Book
Combinatorics and commutative algebra
TL;DR: An overview of the connections between commutative algebra and combinatorics can be found in this article, where the authors present a survey of recent work related to face rings, focusing on applications to f-vectors.
Journal ArticleDOI
Homotopy properties of the poset of nontrivial p-subgroups of a group
TL;DR: In this article, the authors investigated various homotopy invariants of the simplicial complex, such as homology, connectivity, and connectivity of simplicial complexes, for finite groups.
Journal ArticleDOI
Stability of the homology of the mapping class groups of orientable surfaces
TL;DR: The mapping class group of F = Fgs r is F = rgs = wo(A) where A is the topological group of orientation preserving diffeomorphisms of F which are the identity on dF and fix the s punctures as mentioned in this paper.