Basic Concepts of Synthetic Differential Geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Springer US
1996
|
| Series: | Kluwer Texts in the Mathematical Sciences, A Graduate-Level Book Series
13 |
| Subjects: | |
| Online Access: | BTU01 TUM01 UBA01 UBT01 Volltext |
| Item Description: | Starting at an introductory level, the book leads rapidly to important and often new results in synthetic differential geometry. From rudimentary analysis the book moves to such important results as: a new proof of De Rham's theorem; the synthetic view of global action, going as far as the Weil characteristic homomorphism; the systematic account of structured Lie objects, such as Riemannian, symplectic, or Poisson Lie objects; the view of global Lie algebras as Lie algebras of a Lie group in the synthetic sense; and lastly the synthetic construction of symplectic structure on the cotangent bundle in general. Thus while the book is limited to a naive point of view developing synthetic differential geometry as a theory in itself, the author nevertheless treats somewhat advanced topics, which are classic in classical differential geometry but new in the synthetic context. Audience: The book is suitable as an introduction to synthetic differential geometry for students as well as more qualified mathematicians |
| Physical Description: | 1 Online-Ressource (XV, 320 p) |
| ISBN: | 9781475745887 |
| ISSN: | 0927-4529 |
| DOI: | 10.1007/978-1-4757-4588-7 |
Staff View
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Record in the Search Index
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| author_variant | r l rl |
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| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-4588-7 |
| format | Electronic eBook |
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| id | DE-604.BV042421628 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9781475745887 |
| issn | 0927-4529 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857045 |
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| physical | 1 Online-Ressource (XV, 320 p) |
| psigel | ZDB-2-SMA ZDB-2-SMA_Archive |
| publishDate | 1996 |
| publishDateSearch | 1996 |
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| publisher | Springer US |
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| series2 | Kluwer Texts in the Mathematical Sciences, A Graduate-Level Book Series |
| spelling | Lavendhomme, René Verfasser aut Basic Concepts of Synthetic Differential Geometry by René Lavendhomme Boston, MA Springer US 1996 1 Online-Ressource (XV, 320 p) txt rdacontent c rdamedia cr rdacarrier Kluwer Texts in the Mathematical Sciences, A Graduate-Level Book Series 13 0927-4529 Starting at an introductory level, the book leads rapidly to important and often new results in synthetic differential geometry. From rudimentary analysis the book moves to such important results as: a new proof of De Rham's theorem; the synthetic view of global action, going as far as the Weil characteristic homomorphism; the systematic account of structured Lie objects, such as Riemannian, symplectic, or Poisson Lie objects; the view of global Lie algebras as Lie algebras of a Lie group in the synthetic sense; and lastly the synthetic construction of symplectic structure on the cotangent bundle in general. Thus while the book is limited to a naive point of view developing synthetic differential geometry as a theory in itself, the author nevertheless treats somewhat advanced topics, which are classic in classical differential geometry but new in the synthetic context. Audience: The book is suitable as an introduction to synthetic differential geometry for students as well as more qualified mathematicians Mathematics Algebra Global differential geometry Logic, Symbolic and mathematical Cell aggregation / Mathematics Differential Geometry Category Theory, Homological Algebra Mathematical Logic and Foundations Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Synthetische Differentialgeometrie (DE-588)4462361-6 gnd rswk-swf Synthetische Differentialgeometrie (DE-588)4462361-6 s 1\p DE-604 Erscheint auch als Druckausgabe 978-1-4419-4756-7 https://doi.org/10.1007/978-1-4757-4588-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lavendhomme, René Basic Concepts of Synthetic Differential Geometry Mathematics Algebra Global differential geometry Logic, Symbolic and mathematical Cell aggregation / Mathematics Differential Geometry Category Theory, Homological Algebra Mathematical Logic and Foundations Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Synthetische Differentialgeometrie (DE-588)4462361-6 gnd |
| subject_GND | (DE-588)4462361-6 |
| title | Basic Concepts of Synthetic Differential Geometry |
| title_auth | Basic Concepts of Synthetic Differential Geometry |
| title_exact_search | Basic Concepts of Synthetic Differential Geometry |
| title_full | Basic Concepts of Synthetic Differential Geometry by René Lavendhomme |
| title_fullStr | Basic Concepts of Synthetic Differential Geometry by René Lavendhomme |
| title_full_unstemmed | Basic Concepts of Synthetic Differential Geometry by René Lavendhomme |
| title_short | Basic Concepts of Synthetic Differential Geometry |
| title_sort | basic concepts of synthetic differential geometry |
| topic | Mathematics Algebra Global differential geometry Logic, Symbolic and mathematical Cell aggregation / Mathematics Differential Geometry Category Theory, Homological Algebra Mathematical Logic and Foundations Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Synthetische Differentialgeometrie (DE-588)4462361-6 gnd |
| topic_facet | Mathematics Algebra Global differential geometry Logic, Symbolic and mathematical Cell aggregation / Mathematics Differential Geometry Category Theory, Homological Algebra Mathematical Logic and Foundations Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Synthetische Differentialgeometrie |
| url | https://doi.org/10.1007/978-1-4757-4588-7 |
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