A short course in differential topology:
Manifolds are abound in mathematics and physics, and increasingly in cybernetics and visualization where they often reflect properties of complex systems and their configurations. Differential topology gives us the tools to study these spaces and extract information about the underlying systems. Thi...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2018
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| Schriftenreihe: | Cambridge mathematical textbooks
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| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBA01 Volltext |
| Zusammenfassung: | Manifolds are abound in mathematics and physics, and increasingly in cybernetics and visualization where they often reflect properties of complex systems and their configurations. Differential topology gives us the tools to study these spaces and extract information about the underlying systems. This book offers a concise and modern introduction to the core topics of differential topology for advanced undergraduates and beginning graduate students. It covers the basics on smooth manifolds and their tangent spaces before moving on to regular values and transversality, smooth flows and differential equations on manifolds, and the theory of vector bundles and locally trivial fibrations. The final chapter gives examples of local-to-global properties, a short introduction to Morse theory and a proof of Ehresmann's fibration theorem. The treatment is hands-on, including many concrete examples and exercises woven into the text, with hints provided to guide the student |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 28 Jun 2018) Smooth manifolds -- The tangent space -- Regular values -- Vector bundles -- Constructions on vector bundles -- Integrability -- Local phenomena that go global |
| Beschreibung: | 1 Online-Ressource (xii, 251 Seiten) |
| ISBN: | 9781108349130 |
| DOI: | 10.1017/9781108349130 |
Internformat
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| 500 | |a Smooth manifolds -- The tangent space -- Regular values -- Vector bundles -- Constructions on vector bundles -- Integrability -- Local phenomena that go global | ||
| 520 | |a Manifolds are abound in mathematics and physics, and increasingly in cybernetics and visualization where they often reflect properties of complex systems and their configurations. Differential topology gives us the tools to study these spaces and extract information about the underlying systems. This book offers a concise and modern introduction to the core topics of differential topology for advanced undergraduates and beginning graduate students. It covers the basics on smooth manifolds and their tangent spaces before moving on to regular values and transversality, smooth flows and differential equations on manifolds, and the theory of vector bundles and locally trivial fibrations. The final chapter gives examples of local-to-global properties, a short introduction to Morse theory and a proof of Ehresmann's fibration theorem. The treatment is hands-on, including many concrete examples and exercises woven into the text, with hints provided to guide the student | ||
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Datensatz im Suchindex
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| author | Dundas, Bjørn Ian 1963- |
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| dewey-full | 514/.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.72 |
| dewey-search | 514/.72 |
| dewey-sort | 3514 272 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/9781108349130 |
| format | Electronic eBook |
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| isbn | 9781108349130 |
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| spelling | Dundas, Bjørn Ian 1963- Verfasser (DE-588)1034375113 aut A short course in differential topology Bjørn Ian Dundas, Universitetet i Bergen, Norway Cambridge Cambridge University Press 2018 1 Online-Ressource (xii, 251 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge mathematical textbooks Title from publisher's bibliographic system (viewed on 28 Jun 2018) Smooth manifolds -- The tangent space -- Regular values -- Vector bundles -- Constructions on vector bundles -- Integrability -- Local phenomena that go global Manifolds are abound in mathematics and physics, and increasingly in cybernetics and visualization where they often reflect properties of complex systems and their configurations. Differential topology gives us the tools to study these spaces and extract information about the underlying systems. This book offers a concise and modern introduction to the core topics of differential topology for advanced undergraduates and beginning graduate students. It covers the basics on smooth manifolds and their tangent spaces before moving on to regular values and transversality, smooth flows and differential equations on manifolds, and the theory of vector bundles and locally trivial fibrations. The final chapter gives examples of local-to-global properties, a short introduction to Morse theory and a proof of Ehresmann's fibration theorem. The treatment is hands-on, including many concrete examples and exercises woven into the text, with hints provided to guide the student Differential topology Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Differentialgeometrie (DE-588)4012248-7 s 2\p DE-604 Erscheint auch als Druck-Ausgabe 9781108425797 https://doi.org/10.1017/9781108349130 Verlag URL des Erstveröffentlichers 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 | Dundas, Bjørn Ian 1963- A short course in differential topology Differential topology Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4123623-3 |
| title | A short course in differential topology |
| title_auth | A short course in differential topology |
| title_exact_search | A short course in differential topology |
| title_full | A short course in differential topology Bjørn Ian Dundas, Universitetet i Bergen, Norway |
| title_fullStr | A short course in differential topology Bjørn Ian Dundas, Universitetet i Bergen, Norway |
| title_full_unstemmed | A short course in differential topology Bjørn Ian Dundas, Universitetet i Bergen, Norway |
| title_short | A short course in differential topology |
| title_sort | a short course in differential topology |
| topic | Differential topology Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Differential topology Differentialgeometrie Lehrbuch |
| url | https://doi.org/10.1017/9781108349130 |
| work_keys_str_mv | AT dundasbjørnian ashortcourseindifferentialtopology |