Sheaf Theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1997
|
| Edition: | Second Edition |
| Series: | Graduate Texts in Mathematics
170 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 |
| Physical Description: | 1 Online-Ressource (XI, 504 p) |
| ISBN: | 9781461206477 9781461268543 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-0647-7 |
Staff View
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0647-7 |
| edition | Second Edition |
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| id | DE-604.BV042419584 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461206477 9781461268543 |
| issn | 0072-5285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855001 |
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| publisher | Springer New York |
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| series | Graduate Texts in Mathematics |
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| spelling | Bredon, Glen E. 1932-2000 Verfasser (DE-588)1013248945 aut Sheaf Theory by Glen E. Bredon Second Edition New York, NY Springer New York 1997 1 Online-Ressource (XI, 504 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 170 0072-5285 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 Mathematics Algebraic topology Algebraic Topology Mathematik Garbe Mathematik (DE-588)4019261-1 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Garbentheorie (DE-588)4155956-3 gnd rswk-swf Kohomologie (DE-588)4031700-6 gnd rswk-swf Homologie (DE-588)4141951-0 gnd rswk-swf Garbe Mathematik (DE-588)4019261-1 s 1\p DE-604 Garbentheorie (DE-588)4155956-3 s 2\p DE-604 Algebraische Topologie (DE-588)4120861-4 s 3\p DE-604 Homologie (DE-588)4141951-0 s 4\p DE-604 Kohomologie (DE-588)4031700-6 s 5\p DE-604 Graduate Texts in Mathematics 170 (DE-604)BV035421258 170 https://doi.org/10.1007/978-1-4612-0647-7 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bredon, Glen E. 1932-2000 Sheaf Theory Graduate Texts in Mathematics Mathematics Algebraic topology Algebraic Topology Mathematik Garbe Mathematik (DE-588)4019261-1 gnd Algebraische Topologie (DE-588)4120861-4 gnd Garbentheorie (DE-588)4155956-3 gnd Kohomologie (DE-588)4031700-6 gnd Homologie (DE-588)4141951-0 gnd |
| subject_GND | (DE-588)4019261-1 (DE-588)4120861-4 (DE-588)4155956-3 (DE-588)4031700-6 (DE-588)4141951-0 |
| title | Sheaf Theory |
| title_auth | Sheaf Theory |
| title_exact_search | Sheaf Theory |
| title_full | Sheaf Theory by Glen E. Bredon |
| title_fullStr | Sheaf Theory by Glen E. Bredon |
| title_full_unstemmed | Sheaf Theory by Glen E. Bredon |
| title_short | Sheaf Theory |
| title_sort | sheaf theory |
| topic | Mathematics Algebraic topology Algebraic Topology Mathematik Garbe Mathematik (DE-588)4019261-1 gnd Algebraische Topologie (DE-588)4120861-4 gnd Garbentheorie (DE-588)4155956-3 gnd Kohomologie (DE-588)4031700-6 gnd Homologie (DE-588)4141951-0 gnd |
| topic_facet | Mathematics Algebraic topology Algebraic Topology Mathematik Garbe Mathematik Algebraische Topologie Garbentheorie Kohomologie Homologie |
| url | https://doi.org/10.1007/978-1-4612-0647-7 |
| volume_link | (DE-604)BV035421258 |
| work_keys_str_mv | AT bredonglene sheaftheory |