1,720,982 research outputs found
A geometric description of differential cohomology
Full text linkIn this paper we give a geometric cobordism description of differential integral cohomology. The main motivation to consider this model (for other models see [5, 6, 7, 8]) is that it allows for simple descriptions of both the cup product and the integration. In particular it is very easy to verify the compatibilty of these structures. We proceed in a similar way in the case of differential cobordism as constructed in [4]. There the starting point was Quillen\’s cobordism description of singular cobordism groups for a differential manifold X. Here we use instead the similar description of integral cohomology from [11]. This cohomology theory is denoted by SH (X). In this description smooth manifolds in Quillen\’s description are replaced by so-called stratifolds, which are certain stratified spaces. The cohomology theory SH (X) is naturally isomorphic to ordinary integral cohomology H (X), thus we obtain a cobordism type definition of the differential extension of ordinary integral cohomology
Immersions of punctured 4-manifolds: with applications to quantum cellular automata
No full textMotivated by applications to pulling back quantum cellular automata from one manifold to another, we study the existence of immersions between certain smooth 4-manifolds. We show that they lead to a very interesting partial order on closed 4-manifold
Smooth 4–manifolds and surface diagrams
Full text linkSurface diagrams are a diagrammatic representation of smooth, 4-dimensional manifolds. In fact, a surface diagram encodes a 4-manifold together with a map onto the 2-sphere. After giving a detailed proof of this correspondence, we study the topology of 4-manifolds in terms of the combinatorics of its surface diagrams
On the Classification of Cohomology Bott Manifolds
Full text linkWe study cohomology Bott manifolds by means of modified surgery theory. Cohomology Bott manifolds admit a ring isomorphism to the cohomology ring of a Bott manifold which preserves the Pontrjagin and Stiefel-Whitney classes. We show that the number of diffeomorphism classes of cohomology Bott manifolds is finite and construct first examples of manifolds which are cohomology Bott manifolds but not Bott manifolds. Furthermore, we consider the strong cohomological rigidity problem, i.e. we examine the realisability question for an automorphism of the cohomology ring of a specific Bott manifold
A diffeomorphism classification of 5- and 7-dimensional non-simply-connected homogeneous spaces
Full text linkIn this thesis we classify non-simply-connected smooth closed 5- and 7-dimensional orientable manifolds with finite cyclic fundamental group up to diffeomorphism. The manifolds which we consider admit transitive actions of Lie groups and Einstein metrics of positive scalar curvature. One can describe these manifolds as total spaces of certain principal U(1)-fibre bundles over a product of complex projective spaces
Orientation reversal of manifolds
Full text linkWe study the phenomenon of chirality in the context of manifolds. An orientable manifold is called amphicheiral if it admits an orientation-reversing self-map and chiral if it does not. In addition to being continuous and of degree –1, the self map can be required to be a homotopy equivalence, a homeomorphism or a diffeomorphism. We call a manifold e.g. “smoothly amphicheiral” or “homotopically chiral”, according to the category which is considered. We show that in every dimension greater or equal to 3, there exist manifolds which are chiral in the strongest sense, i.e. which do not admit a self-map of degree –1. Further, we prove that there are simply-connected manifolds without a self-map of degree –1 in every dimension greater or equal to 7. Further results show the existence of homotopically chiral manifolds in every bordism class in dimensions greater or equal to 3. Along with these existence results, we also study the topological obstructions which can prevent orientation reversal. Aiming in the opposite direction, we show that certain products of 3-dimensional lens spaces are smoothly amphicheiral. For every integer k, we exhibit lens spaces whose orientation can be reversed by a diffeomorphism of finite order 2^k but not by any continuous map of smaller order
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
Stratifolds And Equivariant Cohomology Theories
Full text link(co)homology is an important tool for studying spaces with a group action. These (co)homology groups are defined via the Borel construction. For discrete group they can also be defined in terms of homological algebra. One can also define Tate (co)homology for spaces with a finite group action in a similar way. There is a natural transformation from equivariant cohomology to Tate cohomology. In such a situation one naturally asks two questions: 1) Can one say something about the kernel and cokernel of this map? 2) Can one define Tate cohomology groups for spaces when the group acting is not finite but a compact Lie group? To both questions we give an answer in this thesis. The answer to the first question is given by defining a third (co)homology theory called backwards (co)homology and an exact sequence relating all three (co)homology theories. This new theory is a straightforward generalization of the construction of equivariant (co)homology and Tate (co)homology in terms of homological algebra. Of course, this only works for finite groups. The answer to the second question is given in the terms of stratifolds and bordism theories of stratifolds. We construct a long exact sequence which generalizes the sequence discussed above to the case of compact Lie groups. A third question that concerns us is equivariant Poincare duality. Poincare duality does not hold in equivariant (co)homology, even in the case of a point. We show that Tate cohomology is an obstruction for Poincare duality, which means that it holds if and only if Tate cohomology vanishes which is the case if and only if the action is free. We show that equivariant cohomology is Poincare dual to backwards homology, and equivariant homology is Poincare dual to backwards cohomology. The geometric point of view can be used for computations. We give a simple example how one should attack such a problem. In the last part of the thesis we give a geometric interpretation of the product in negative Tate cohomology, again in terms of stratifolds
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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