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Showing 1 to 15 of 15 for “"classifying space"”.
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A Classifying Family of Spaces for the Cohomology of Profinite Groups
… cohomology of a discrete group is that group's classifying space. In some sense, the classifying space captures both the group itself and a description of its cohomology for any action of the group on any coefficient module. While some constructions for a classifying space also apply to …
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Torsors over Simplicial Schemes
… a perfect field, the motivic cohomology of the classifying space BGL_n of the general linear group is a polynomial algebra over the motivic cohomology of k; we give a proof that takes advantage of this theory of torsors over simplicial schemes. Finally, using the work of Vistoli, we prove that, …
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Spaces of homomorphisms and group cohomology
In this work we study the space of group homomorphisms Hom(Γ,G) from a geometric and simplicial point of view. The case in which the source group is a free abelian group of rank n is studied in more detail since this space can be identified with the space of commuting n-tuples of elements from G. …
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Homotopy Theory of Monoids and Group Completion
… isomorphic to the homotopy type of loops on the classifying space of a monoid. We use the Street nerve to show that the derived functor of group completion of monoids in the category of ω-groupoids for the Gray tensor product is isomorphic to group completion for simplicial monoids in low …
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cdh descent for homotopy Hermitian K-Theory of rings with involution
We provide a geometric model for the classifying space of automorphism groups of Hermitian vector bundles over a ring with involution with 2 invertible; this generalizes a result of Schlichting-Tripathi. We then prove a periodicity theorem for Hermitian K-theory and use it to construct an …
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Dual Homotopy Invariants of G-Foliations
… (pi)(,n)(B(GAMMA)('q)) of the corresponding classifying space are shown to map onto (//R)('v(,n)), where {v(,n)} has a subsequence tending to infinity.
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Orbispaces
… thesis, I introduce a new definition for orbispaces based a notion of stratified fibration and prove it's equivalence with other existing definitions. I study the notion of orbispace structures on a given stratified space. I then set up two parallel theories of stratified fibrations, one for …
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Cohomological invariants for infinite groups
… that act on finite-dimensional contractible CW-spaces with finite stabilisers. Important examples of these are given by groups admitting a finite-dimensional classifying space for proper actions EFG. A large part of the thesis is motivated by an old conjecture of Kropholler and Mislin claiming …
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Automorphisms of free products of groups
… and with strong links to geometric configuration spaces. In this thesis I describe in detail and for the first time the (co)homology of the symmetric automorphism groups. To this end I construct a classifying space for the Fouxe-Rabinovitch automorphism group, a large normal subgroup of the …
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An infinite loop space structure for K-theory of bimonoidal categories
… that it is equivalent to the algebraic K-theory space of the ring spectrum KR. In this thesis we show that K(R) is the group completion of the classifying space of the 2-category ModR of modules over R, and show that ModR is a symmetric monoidal 2-category. We explain how to use this symmetric …
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Frobenius transfers and p-local finite groups
… of Broto, Levi and Oliver in terms of their classifying spaces. More precisely, we consider the question posed by Haynes Miller, whether an equivalent theory can be recovered by studying maps f: BS --> X from the classifying space of a finite p-group S to a p-complete space X equipped with a …
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On tautological classes of fibre bundles and self-embedding calculus
… that is sharp. In the second part, we study the classifying space using the calculus of embeddings which provides a homotopy theoretic approximation. We construct cohomology classes on the self-embedding tower which extend certain characteristic classes that were introduced by Kontsevich. This …
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Characterization and properties of some light-open mappings
… class of finite-to-one open maps and show that a classifying space exists for maps in this class, where point inverses consist of either n points or one point, provided a certain type of covering space exists. In addition, we have the following corollary to our work:</p> <p><em>Theorem</em>. A …
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Computational methods for higher real K-theory with applications to tmf
… can be used to compute the tmf homology of a space or spectrum at the prime 3. Generalizing work of Mahowald and Davis, we use this Hopf algebra to compute the tmf homology of the classifying space of the symmetric group on three elements. We also discuss the E3 Tate spectrum of tmf at the …
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On Bredon (co-)homological dimensions of groups
The objects of interest in this thesis are classifying spaces EFG for discrete groups G with stabilisers in a given family F of subgroups of G. The main focus of this thesis lies in the family Fvc(G) of virtually cyclic subgroups of G. A classifying space for this specific family is denoted by EG. …