Mod p homology of the stable mapping class group
نویسندگان
چکیده
منابع مشابه
MOD p HOMOLOGY OF THE STABLE MAPPING CLASS GROUP
We calculate the homology H∗(Γg,n;Fp) of the mapping class group Γg,n in the stable range. The calculation is based on Madsen and Weiss’ proof of the “Generalised Mumford Conjecture”: Γg,n has the same homology as a component of the space Ω∞CP∞ −1 in the stable range.
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We compute the mod 2 homology of spin mapping class groups in the stable range. In earlier work [G] we computed the stable mod p homology of the oriented mapping class group, and the methods and results here are very similar. The forgetful map from the spin mapping class group to the oriented mapping class groups induces a homology isomorphism for odd p but for p = 2 it is far from being an iso...
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The stable mapping class group is the group of isotopy classes of automorphisms of a connected oriented surface of “large” genus. The Mumford conjecture postulates that its rational cohomology is a polynomial ring generated by certain classes κi of dimension 2i, for i > 0. Tillmann’s insight [38] that the plus construction makes the classifying space of the stable mapping class group into an in...
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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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We consider symplectic Floer homology in the lowest nontrivial dimension, that is to say, for area-preserving diffeomorphisms of surfaces. Particular attention is paid to the quantum cap product.
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ژورنال
عنوان ژورنال: Topology
سال: 2004
ISSN: 0040-9383
DOI: 10.1016/j.top.2004.01.011