Synthetic geometry of manifolds:
This elegant book is sure to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighbourhoods of the diagonal. These spaces enable a natural description of some of the basic con...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2010
|
| Schriftenreihe: | Cambridge tracts in mathematics
180 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1017/CBO9780511691690 https://doi.org/10.1017/CBO9780511691690 https://doi.org/10.1017/CBO9780511691690 https://doi.org/10.1017/CBO9780511691690 |
| Zusammenfassung: | This elegant book is sure to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighbourhoods of the diagonal. These spaces enable a natural description of some of the basic constructions in local differential geometry and, in fact, form an inviting gateway to differential geometry, and also to some differential-geometric notions that exist in algebraic geometry. The presentation conveys the real strength of this approach to differential geometry. Concepts are clarified, proofs are streamlined, and the focus on infinitesimal spaces motivates the discussion well. Some of the specific differential-geometric theories dealt with are connection theory (notably affine connections), geometric distributions, differential forms, jet bundles, differentiable groupoids, differential operators, Riemannian metrics, and harmonic maps. Ideal for graduate students and researchers wishing to familiarize themselves with the field |
| Umfang: | 1 Online-Ressource (xiii, 302 Seiten) |
| ISBN: | 9780511691690 |
| DOI: | 10.1017/CBO9780511691690 |
Internformat
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| 490 | 0 | |a Cambridge tracts in mathematics |v 180 | |
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| 520 | |a This elegant book is sure to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighbourhoods of the diagonal. These spaces enable a natural description of some of the basic constructions in local differential geometry and, in fact, form an inviting gateway to differential geometry, and also to some differential-geometric notions that exist in algebraic geometry. The presentation conveys the real strength of this approach to differential geometry. Concepts are clarified, proofs are streamlined, and the focus on infinitesimal spaces motivates the discussion well. Some of the specific differential-geometric theories dealt with are connection theory (notably affine connections), geometric distributions, differential forms, jet bundles, differentiable groupoids, differential operators, Riemannian metrics, and harmonic maps. Ideal for graduate students and researchers wishing to familiarize themselves with the field | ||
| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Manifolds (Mathematics) | |
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Datensatz im Suchindex
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| author | Kock, Anders 1938- |
| author_GND | (DE-588)132017598 |
| author_facet | Kock, Anders 1938- |
| author_role | aut |
| author_sort | Kock, Anders 1938- |
| author_variant | a k ak |
| building | Verbundindex |
| bvnumber | BV043942073 |
| classification_rvk | SK 370 SK 350 |
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| contents | 1. Calculus and linear algebra -- 2. Geometry of the neighbour relation -- 3. Combinatorial differential forms -- 4. The tangent bundle -- 5. Groupoids -- 6. Lie theory; non-abelian covariant derivative -- 7. Jets and differential operators -- 8. Metric notions |
| ctrlnum | (ZDB-20-CBO)CR9780511691690 (OCoLC)967601529 (DE-599)BVBBV043942073 |
| dewey-full | 516.3/62 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/62 |
| dewey-search | 516.3/62 |
| dewey-sort | 3516.3 262 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511691690 |
| format | Electronic eBook |
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| id | DE-604.BV043942073 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:49:18Z |
| institution | BVB |
| isbn | 9780511691690 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351043 |
| oclc_num | 967601529 |
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| physical | 1 Online-Ressource (xiii, 302 Seiten) |
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| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge University Press |
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| series2 | Cambridge tracts in mathematics |
| spelling | Kock, Anders 1938- Verfasser (DE-588)132017598 aut Synthetic geometry of manifolds Anders Kock Cambridge Cambridge University Press 2010 1 Online-Ressource (xiii, 302 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 180 1. Calculus and linear algebra -- 2. Geometry of the neighbour relation -- 3. Combinatorial differential forms -- 4. The tangent bundle -- 5. Groupoids -- 6. Lie theory; non-abelian covariant derivative -- 7. Jets and differential operators -- 8. Metric notions This elegant book is sure to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighbourhoods of the diagonal. These spaces enable a natural description of some of the basic constructions in local differential geometry and, in fact, form an inviting gateway to differential geometry, and also to some differential-geometric notions that exist in algebraic geometry. The presentation conveys the real strength of this approach to differential geometry. Concepts are clarified, proofs are streamlined, and the focus on infinitesimal spaces motivates the discussion well. Some of the specific differential-geometric theories dealt with are connection theory (notably affine connections), geometric distributions, differential forms, jet bundles, differentiable groupoids, differential operators, Riemannian metrics, and harmonic maps. Ideal for graduate students and researchers wishing to familiarize themselves with the field Geometry, Differential Manifolds (Mathematics) Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Differentialgeometrie (DE-588)4012248-7 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-11673-2 https://doi.org/10.1017/CBO9780511691690 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Kock, Anders 1938- Synthetic geometry of manifolds 1. Calculus and linear algebra -- 2. Geometry of the neighbour relation -- 3. Combinatorial differential forms -- 4. The tangent bundle -- 5. Groupoids -- 6. Lie theory; non-abelian covariant derivative -- 7. Jets and differential operators -- 8. Metric notions Geometry, Differential Manifolds (Mathematics) Mannigfaltigkeit (DE-588)4037379-4 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4037379-4 (DE-588)4012248-7 |
| title | Synthetic geometry of manifolds |
| title_auth | Synthetic geometry of manifolds |
| title_exact_search | Synthetic geometry of manifolds |
| title_full | Synthetic geometry of manifolds Anders Kock |
| title_fullStr | Synthetic geometry of manifolds Anders Kock |
| title_full_unstemmed | Synthetic geometry of manifolds Anders Kock |
| title_short | Synthetic geometry of manifolds |
| title_sort | synthetic geometry of manifolds |
| topic | Geometry, Differential Manifolds (Mathematics) Mannigfaltigkeit (DE-588)4037379-4 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Geometry, Differential Manifolds (Mathematics) Mannigfaltigkeit Differentialgeometrie |
| url | https://doi.org/10.1017/CBO9780511691690 |
| work_keys_str_mv | AT kockanders syntheticgeometryofmanifolds |