A First Course in Geometric Topology and Differential Geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1997
|
| Schriftenreihe: | Modern Birkhäuser Classics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This textis anintroduction togeometric topology anddifferentialgeometry via the study of surfaces, and more generally servestointroduce the student to the relation of the modem axiomatic approach in mathematics to geometric intu ition. The idea of combining geometry and topology in a text ,of iscourse,not new;the present text attempts to make such a combination of subjects accessi bletothejunior/seniorlevelmathematics majoratauniversityorcollegeinthe UnitedStates . Though someofthedeepconnections betweenthetopology and geometry of manifolds can only bedealt withusing more advancedtechniques thanthose presented here, wedoreachtheclassical Gauss -BonnetTheorem a model theorem for the relation of topology andgeometry- attheend of the book. The notion of a surface is the unifyingread th of the text. Our treatment of point set topology is brief and restricted to subsets of Euclidean spaces; the discussion of topological surfaces is geometric rather than algebraic ; the treatment of differential geometry is classical, treating surfaces JR3. in The goal of the book is to reach a number of intuitively appealing definitions and theorems concerning surfaces in the topological, polyhedral and smooth. cases Some of the goodies aimed at are the classification of compact surfaces, the Gauss-BonnetTheorem(polyhedral and smooth) and the geodesic nature of length-minimizingcurves on surfaces. Only those definitions and methods needed for these ends are developed . In order to keep the discussion at a concrete level, we avoid treating a number of technicalities such as abstract topological spaces, abstract simplicial complexes and tensors |
| Beschreibung: | 1 Online-Ressource (XII, 421 p) |
| ISBN: | 9780817681227 9780817681210 |
| ISSN: | 2197-1803 |
| DOI: | 10.1007/978-0-8176-8122-7 |
Internformat
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| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Geometry | |
| 650 | 4 | |a Global differential geometry | |
| 650 | 4 | |a Topology | |
| 650 | 4 | |a Differential Geometry | |
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Datensatz im Suchindex
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| dewey-full | 516 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516 |
| dewey-search | 516 |
| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-0-8176-8122-7 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9780817681227 9780817681210 |
| issn | 2197-1803 |
| language | English |
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| physical | 1 Online-Ressource (XII, 421 p) |
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| publishDate | 1997 |
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| spelling | Bloch, Ethan D. Verfasser aut A First Course in Geometric Topology and Differential Geometry by Ethan D. Bloch Boston, MA Birkhäuser Boston 1997 1 Online-Ressource (XII, 421 p) txt rdacontent c rdamedia cr rdacarrier Modern Birkhäuser Classics 2197-1803 This textis anintroduction togeometric topology anddifferentialgeometry via the study of surfaces, and more generally servestointroduce the student to the relation of the modem axiomatic approach in mathematics to geometric intu ition. The idea of combining geometry and topology in a text ,of iscourse,not new;the present text attempts to make such a combination of subjects accessi bletothejunior/seniorlevelmathematics majoratauniversityorcollegeinthe UnitedStates . Though someofthedeepconnections betweenthetopology and geometry of manifolds can only bedealt withusing more advancedtechniques thanthose presented here, wedoreachtheclassical Gauss -BonnetTheorem a model theorem for the relation of topology andgeometry- attheend of the book. The notion of a surface is the unifyingread th of the text. Our treatment of point set topology is brief and restricted to subsets of Euclidean spaces; the discussion of topological surfaces is geometric rather than algebraic ; the treatment of differential geometry is classical, treating surfaces JR3. in The goal of the book is to reach a number of intuitively appealing definitions and theorems concerning surfaces in the topological, polyhedral and smooth. cases Some of the goodies aimed at are the classification of compact surfaces, the Gauss-BonnetTheorem(polyhedral and smooth) and the geodesic nature of length-minimizingcurves on surfaces. Only those definitions and methods needed for these ends are developed . In order to keep the discussion at a concrete level, we avoid treating a number of technicalities such as abstract topological spaces, abstract simplicial complexes and tensors Mathematics Geometry Global differential geometry Topology Differential Geometry Mathematik Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Geometrische Topologie (DE-588)4156724-9 gnd rswk-swf Geometrische Topologie (DE-588)4156724-9 s 1\p DE-604 Differentialgeometrie (DE-588)4012248-7 s 2\p DE-604 https://doi.org/10.1007/978-0-8176-8122-7 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 |
| spellingShingle | Bloch, Ethan D. A First Course in Geometric Topology and Differential Geometry Mathematics Geometry Global differential geometry Topology Differential Geometry Mathematik Differentialgeometrie (DE-588)4012248-7 gnd Geometrische Topologie (DE-588)4156724-9 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4156724-9 |
| title | A First Course in Geometric Topology and Differential Geometry |
| title_auth | A First Course in Geometric Topology and Differential Geometry |
| title_exact_search | A First Course in Geometric Topology and Differential Geometry |
| title_full | A First Course in Geometric Topology and Differential Geometry by Ethan D. Bloch |
| title_fullStr | A First Course in Geometric Topology and Differential Geometry by Ethan D. Bloch |
| title_full_unstemmed | A First Course in Geometric Topology and Differential Geometry by Ethan D. Bloch |
| title_short | A First Course in Geometric Topology and Differential Geometry |
| title_sort | a first course in geometric topology and differential geometry |
| topic | Mathematics Geometry Global differential geometry Topology Differential Geometry Mathematik Differentialgeometrie (DE-588)4012248-7 gnd Geometrische Topologie (DE-588)4156724-9 gnd |
| topic_facet | Mathematics Geometry Global differential geometry Topology Differential Geometry Mathematik Differentialgeometrie Geometrische Topologie |
| url | https://doi.org/10.1007/978-0-8176-8122-7 |
| work_keys_str_mv | AT blochethand afirstcourseingeometrictopologyanddifferentialgeometry |