منابع مشابه
Mod 2 Homology of the Stable Spin Mapping Class Group
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...
متن کاملLoop Space Homology Associated to the Mod 2 Dickson Invariants
The spaces BG2 and BDI(4) have the property that their mod 2 cohomology is given by the rank 3 and 4 Dickson invariants respectively. Associated with these spaces one has for q odd the classifying spaces of the finite groups BG2(q) and the exotic family of classifying spaces of 2-local finite groups BSol(q). In this article we compute the loop space homology of BG2(q) ∧ 2 and BSol(q) for all od...
متن کاملSingular Surfaces, Mod 2 Homology, and Hyperbolic Volume, I
The main theorem of this paper states that if M is a closed orientable hyperbolic 3-manifold of volume at most 3.08, then the rank of H1(M ;Z/2Z) is at most 10. The theorem depends on a purely topological result which can be viewed as an analogue of Dehn’s lemma for π1-injective singular surfaces of genus 2. The proof of the main theorem combines this topological result with several deep geomet...
متن کاملSingular Surfaces, Mod 2 Homology, and Hyperbolic Volume, Ii
The main theorem of this paper states that ifM is a closed orientable hyperbolic 3-manifold of volume at most 3.08, then the dimension of H1(M ;Z2) is at most 7, and that it is at most 6 unless M is “strange.” To say that a closed, orientable 3-manifold M , for which H1(M ;Z2) has dimension 7, is strange means that the Z2-vector space H1(M ;Z2) has a 2-dimensional subspace X such that for every...
متن کاملThe mod 2 homology of the general linear goup of a 2-adic local field
Let F be a finite extension of Q2, of degree d. Our first main theorem gives an explicit computation of the mod two homology Hopf algebra of the infinite general linear group GLF . The answer is formulated in terms of the well-known homology algebras of the infinite unitary group U, its classifying space BU, and the classifying space BO of the infinite orthogonal group. Let P denote the subalge...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-05216-8