1,720,985 research outputs found
Homological algebra with locally compact abelian groups
No full textAbstractIn this article we study locally compact abelian groups using the language of derived categories. We define a derived Hom-functor on the bounded derived category of LCA groups with values in the derived category of Hausdorff topological abelian groups. We introduce a smallness condition for LCA groups and show that the category of such groups has a natural tensor product and internal Hom. Derived versions of these yield closed tensor triangulated categories which may be of arithmetical interest
Periodic twisted cohomology and hBduality
No full textUsing the differentiable structure, twisted 2-periodic de Rham cohomology is well known, and showing up as the target of Chern characters for twisted K-theory. The main motivation of this work is a topological interpretation of two-periodic twisted de Rham cohomology which is generalizable to arbitrary topological spaces and at the same time to arbitrary coefficients. To this end we develop a sheaf theory in the context of locally compact topological stacks with emphasis on: the construction of the sheaf theory operations in unbounded derived categories elements of Verdier duality and integration. The main result is the construction of a functorial periodization associated to a U(1)-gerbe. As an application we verify the T-duality isomorphism in periodic twisted cohomology and in periodic twisted orbispace cohomology
Periodic twisted cohomology and hBduality
No full textUsing the differentiable structure, twisted 2-periodic de Rham cohomology is well known, and showing up as the target of Chern characters for twisted K-theory. The main motivation of this work is a topological interpretation of two-periodic twisted de Rham cohomology which is generalizable to arbitrary topological spaces and at the same time to arbitrary coefficients. To this end we develop a sheaf theory in the context of locally compact topological stacks with emphasis on: the construction of the sheaf theory operations in unbounded derived categories elements of Verdier duality and integration. The main result is the construction of a functorial periodization associated to a U(1)-gerbe. As an application we verify the T-duality isomorphism in periodic twisted cohomology and in periodic twisted orbispace cohomology
Sheaf theory for stacks in manifolds and twisted cohomology for ^1hBHgerbes
No full textIn this paper we give a sheaf theory interpretation of the twisted cohomology of manifolds. To this end we develop a sheaf theory on smooth stacks. The derived push-forward of the constant sheaf with value R along the structure map of a U(1) gerbe over a smooth manifold X is an object of the derived category of sheaves on X. Our main result shows that it is isomorphic in this derived category to a sheaf of twisted de Rham complexes
Duality for topological abelian group stacks and ehBduality
No full textWe extend Pontrjagin duality from topological abelian groups to certain locally compact group stacks. To this end we develop a sheaf theory on the big site of topological spaces S in order to prove that the sheaves ExtiShAbS(G,T), i = 1, 2, vanish, where G is the sheaf represented by a locally compact abelian group and T is the circle. As an application of the theory we interpret topological T-duality of principal Tn-bundles in terms of Pontrjagin duality of abelian group stacks
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Homotopy limits of model categories over inverse index categories
No full textAbstractIn this note we give a model category theoretic interpretation of the homotopy colimit of the diagram of simplicial localizations coming from a diagram of model categories in the case of an inverse indexing category
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