Sheaves in Topology:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2004
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XVI, 240 p) |
| ISBN: | 9783642188688 9783540206651 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-3-642-18868-8 |
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| 500 | |a 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 | ||
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-search | 516.35 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-18868-8 |
| format | Electronic eBook |
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| isbn | 9783642188688 9783540206651 |
| issn | 0172-5939 |
| language | English |
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| spelling | Dimca, Alexandru Verfasser aut Sheaves in Topology by Alexandru Dimca Berlin, Heidelberg Springer Berlin Heidelberg 2004 1 Online-Ressource (XVI, 240 p) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 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 Mathematics Geometry, algebraic Differential equations, partial Algebraic topology Algebraic Geometry Several Complex Variables and Analytic Spaces Algebraic Topology Mathematik Kohomologietheorie (DE-588)4164610-1 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Garbe Mathematik (DE-588)4019261-1 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 s Garbe Mathematik (DE-588)4019261-1 s 1\p DE-604 Kohomologietheorie (DE-588)4164610-1 s 2\p DE-604 https://doi.org/10.1007/978-3-642-18868-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dimca, Alexandru Sheaves in Topology Mathematics Geometry, algebraic Differential equations, partial Algebraic topology Algebraic Geometry Several Complex Variables and Analytic Spaces Algebraic Topology Mathematik Kohomologietheorie (DE-588)4164610-1 gnd Algebraische Topologie (DE-588)4120861-4 gnd Garbe Mathematik (DE-588)4019261-1 gnd |
| subject_GND | (DE-588)4164610-1 (DE-588)4120861-4 (DE-588)4019261-1 |
| title | Sheaves in Topology |
| title_auth | Sheaves in Topology |
| title_exact_search | Sheaves in Topology |
| title_full | Sheaves in Topology by Alexandru Dimca |
| title_fullStr | Sheaves in Topology by Alexandru Dimca |
| title_full_unstemmed | Sheaves in Topology by Alexandru Dimca |
| title_short | Sheaves in Topology |
| title_sort | sheaves in topology |
| topic | Mathematics Geometry, algebraic Differential equations, partial Algebraic topology Algebraic Geometry Several Complex Variables and Analytic Spaces Algebraic Topology Mathematik Kohomologietheorie (DE-588)4164610-1 gnd Algebraische Topologie (DE-588)4120861-4 gnd Garbe Mathematik (DE-588)4019261-1 gnd |
| topic_facet | Mathematics Geometry, algebraic Differential equations, partial Algebraic topology Algebraic Geometry Several Complex Variables and Analytic Spaces Algebraic Topology Mathematik Kohomologietheorie Algebraische Topologie Garbe Mathematik |
| url | https://doi.org/10.1007/978-3-642-18868-8 |
| work_keys_str_mv | AT dimcaalexandru sheavesintopology |