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Faisceaux, Théorie des --- Sheaf theory. --- Topologie algebrique --- Homologie et cohomologie --- Topologie algebrique --- Homologie et cohomologie
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Algebraic topology. --- Sheaf theory. --- Topologie algébrique --- Faisceaux, Théorie des --- Geometrie algebrique --- Geometrie algebrique
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Algebraic topology. --- Sheaf theory. --- Topologie algébrique --- Faisceaux, Théorie des --- Topologie algebrique --- Homologie et cohomologie --- Topologie algebrique --- Homologie et cohomologie
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Algebraic topology. --- Sheaf theory. --- Topologie algébrique --- Faisceaux, Théorie des --- Topologie algebrique --- Homologie et cohomologie --- Topologie algebrique --- Homologie et cohomologie
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Analytical spaces --- Duality theory (Mathematics) --- Linear topological spaces. --- Vector bundles. --- Duality theory (Mathematics). --- Algebraic topology --- Sheaf theory --- Topologie algébrique --- Faisceaux, Théorie des --- Topologie algébrique --- Faisceaux, Théorie des --- Espaces vectoriels topologiques --- Linear topological spaces --- Topologie algébrique. --- Faisceaux, Théorie des. --- Faisceaux, Théorie des.
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Sheaf theory. --- Induction (Mathematics) --- Abelian categories. --- Sheaf theory --- Integral transforms --- D-modules --- Faisceaux, Théorie des. --- Transformations intégrales. --- D-modules, Théorie des. --- Faisceaux, Théorie des. --- Transformations intégrales. --- D-modules, Théorie des.
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This book is primarily concerned with the study of cohomology theories of general topological spaces with "general coefficient systems." Sheaves play several roles in this study. For example, they provide a suitable notion of "general coefficient systems." Moreover, they furnish us with a common method of defining various cohomology theories and of comparison between different cohomology theories. The parts of the theory of sheaves covered here are those areas important to algebraic topology. Sheaf theory is also important in other fields of mathematics, notably algebraic geometry, but that is outside the scope of the present book. Thus a more descriptive title for this book might have been Algebraic Topology from the Point of View of Sheaf Theory. Several innovations will be found in this book. Notably, the concept of the "tautness" of a subspace (an adaptation of an analogous notion of Spanier to sheaf-theoretic cohomology) is introduced and exploited throughout the book. The fact that sheaf-theoretic cohomology satisfies 1 the homotopy property is proved for general topological spaces. Also, relative cohomology is introduced into sheaf theory. Concerning relative cohomology, it should be noted that sheaf-theoretic cohomology is usually considered as a "single space" theory.
Sheaf theory --- Théorie des faisceaux --- Algebraic topology --- Topologie algébrique --- Faisceaux, Théorie des --- Algebra. --- Algebraic topology. --- Algebraic Topology. --- Topology --- Mathematics --- Mathematical analysis --- Sheaf theory. --- Topologie algébrique --- Faisceaux, Théorie des --- Topologie algebrique --- Homologie et cohomologie
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Algebraic topology. --- Sheaf theory. --- Topologie algébrique --- Faisceaux, Théorie des --- Algèbre homologique --- Algebra, Homological. --- Topologie algebrique --- Topologie algebrique --- Homologie et cohomologie --- Topologie algebrique --- Topologie algebrique --- Homologie et cohomologie
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D-module theory is essentially the algebraic study of systems of linear partial differential equations. This book, the first devoted specifically to holonomic D-modules, provides a unified treatment of both regular and irregular D-modules. The authors begin by recalling the main results of the theory of indsheaves and subanalytic sheaves, explaining in detail the operations on D-modules and their tempered holomorphic solutions. As an application, they obtain the Riemann-Hilbert correspondence for regular holonomic D-modules. In the second part of the book the authors do the same for the sheaf of enhanced tempered solutions of (not necessarily regular) holonomic D-modules. Originating from a series of lectures given at the Institut des Hautes Études Scientifiques in Paris, this book is addressed to graduate students and researchers familiar with the language of sheaves and D-modules, in the derived sense.
D-modules. --- Modules (Algebra) --- Sheaf theory. --- Geometry, Algebraic. --- Algebraic geometry --- Geometry --- Cohomology, Sheaf --- Sheaf cohomology --- Sheaves, Theory of --- Sheaves (Algebraic topology) --- Algebraic topology --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Rings (Algebra) --- D-modules, Théorie des. --- Modules (algèbre) --- Faisceaux, Théorie des. --- Géométrie algébrique.
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Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties). This introduction to the subject can be regarded as a textbook on "Modern Algebraic Topology'', which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology). The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements. Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.
Sheaf theory --- 515.14 --- Cohomology, Sheaf --- Sheaf cohomology --- Sheaves, Theory of --- Sheaves (Algebraic topology) --- Algebraic topology --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- 515.14 Algebraic topology --- Sheaf theory. --- Topologie algébrique --- Faisceaux, Théorie des --- Algebraic topology. --- Algebraic geometry. --- Functions of complex variables. --- Algebraic Topology. --- Algebraic Geometry. --- Several Complex Variables and Analytic Spaces. --- Complex variables --- Elliptic functions --- Functions of real variables --- Algebraic geometry --- Topology --- Topologie algébrique --- Faisceaux, Théorie des --- Faisceaux --- Geometrie algebrique --- Topologie algebrique --- Cohomologie --- Homologie et cohomologie
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