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Showing 1 to 9 of 9 for “"Group Cohomology"”.
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Finiteness conditions in group cohomology
In this thesis we investigate groups whose nth cohomology functors commute with filtered colimits for all sufficiently large n. In Chapter 1 we introduce some basic definitions and important background material. We make the definition that a group G has cohomology almost everywhere finitary if and …
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Universal Localization and Group Cohomology
… coincide. Second, for an infinite discrete group G, we investigate group cohomology and homology with coefficients in lp(G). We prove that if G is of type FPn, then all its homology and cohomology groups up to n are either zero or infinite dimensional. This generalizes one of the results …
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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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Quillen cohomology of pi-algebras and application to their realization by Martin Frankland.
… space of certain - algebras with 2 non-trivial groups. The main technical tool is a result on the Quillen cohomology of truncated -algebras, which is an instance of comparison map induced by an adjunction. We study in more generality the behavior of Quillen (co)homology with respect to …
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L-functions and J-spectra
… χ via the Dieudonné theory of height 1 formal groups and formal A-modules and their finite subgroups. Our approach is based on Katz’s algebro-geometric explanation of p-adic congruences of normalized Eisenstein series E_2k of level 1. The crucial step is to translate the Dirichlet character χ …
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Cohomological invariants for infinite groups
… main objects of interest in this thesis are H1F-groups. These are 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 …
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Aspects of symmetry, topology and anomalies in quantum matter
… of SPT invariants in any dimension to uncover group cohomology classification and beyond -- the former for SPTs with gapless boundary gauge anomalies, the latter for SPTs with mixed gauge-gravity anomalies. We study topological orders in 3+1 dimensions such as Dijkgraaf-Witten models, which …
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First Cohomology of Some Infinitely Generated Groups
The goal of this paper is to explore the first cohomology group of groups G that are not necessarily finitely generated. Our focus is on l^p-cohomology, 1 leq p leq infty, and what results regarding finitely generated groups change when G is infinitely generated. In particular, for abelian groups …
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First l²-Cohomology Groups
We want to take a look at the first cohomology group H^1(G, l^2(G)), in particular when G is locally-finite. First, though, we discuss some results about the space H^1(G, C G) for G locally-finite, as well as the space H^1(G, l^2(G)) when G is finitely generated. We show that, although in the case …