Differential Topology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1976
|
| Series: | Graduate Texts in Mathematics
33 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | This book presents some of the basic topological ideas used in studying differentiable manifolds and maps. Mathematical prerequisites have been kept to a minimum; the standard course in analysis and general topology is adequate preparation. An appendix briefly summarizes some of the back ground material. In order to emphasize the geometrical and intuitive aspects of differen tial topology, I have avoided the use of algebraic topology, except in a few isolated places that can easily be skipped. For the same reason I make no use of differential forms or tensors. In my view, advanced algebraic techniques like homology theory are better understood after one has seen several examples of how the raw material of geometry and analysis is distilled down to numerical invariants, such as those developed in this book: the degree of a map, the Euler number of a vector bundle, the genus of a surface, the cobordism class of a manifold, and so forth. With these as motivating examples, the use of homology and homotopy theory in topology should seem quite natural. There are hundreds of exercises, ranging in difficulty from the routine to the unsolved. While these provide examples and further developments of the theory, they are only rarely relied on in the proofs of theorems |
| Physical Description: | 1 Online-Ressource (X, 222 p) |
| ISBN: | 9781468494495 9781468494518 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4684-9449-5 |
Staff View
MARC
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| 500 | |a This book presents some of the basic topological ideas used in studying differentiable manifolds and maps. Mathematical prerequisites have been kept to a minimum; the standard course in analysis and general topology is adequate preparation. An appendix briefly summarizes some of the back ground material. In order to emphasize the geometrical and intuitive aspects of differen tial topology, I have avoided the use of algebraic topology, except in a few isolated places that can easily be skipped. For the same reason I make no use of differential forms or tensors. In my view, advanced algebraic techniques like homology theory are better understood after one has seen several examples of how the raw material of geometry and analysis is distilled down to numerical invariants, such as those developed in this book: the degree of a map, the Euler number of a vector bundle, the genus of a surface, the cobordism class of a manifold, and so forth. With these as motivating examples, the use of homology and homotopy theory in topology should seem quite natural. There are hundreds of exercises, ranging in difficulty from the routine to the unsolved. While these provide examples and further developments of the theory, they are only rarely relied on in the proofs of theorems | ||
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Record in the Search Index
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| dewey-full | 514.34 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-9449-5 |
| format | Electronic eBook |
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| spelling | Hirsch, Morris W. 1933- Verfasser (DE-588)172139120 aut Differential Topology by Morris W. Hirsch New York, NY Springer New York 1976 1 Online-Ressource (X, 222 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 33 0072-5285 This book presents some of the basic topological ideas used in studying differentiable manifolds and maps. Mathematical prerequisites have been kept to a minimum; the standard course in analysis and general topology is adequate preparation. An appendix briefly summarizes some of the back ground material. In order to emphasize the geometrical and intuitive aspects of differen tial topology, I have avoided the use of algebraic topology, except in a few isolated places that can easily be skipped. For the same reason I make no use of differential forms or tensors. In my view, advanced algebraic techniques like homology theory are better understood after one has seen several examples of how the raw material of geometry and analysis is distilled down to numerical invariants, such as those developed in this book: the degree of a map, the Euler number of a vector bundle, the genus of a surface, the cobordism class of a manifold, and so forth. With these as motivating examples, the use of homology and homotopy theory in topology should seem quite natural. There are hundreds of exercises, ranging in difficulty from the routine to the unsolved. While these provide examples and further developments of the theory, they are only rarely relied on in the proofs of theorems Mathematics Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Differentialtopologie (DE-588)4012255-4 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 1976 Varenna gnd-content Differentialtopologie (DE-588)4012255-4 s 2\p DE-604 https://doi.org/10.1007/978-1-4684-9449-5 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 | Hirsch, Morris W. 1933- Differential Topology Mathematics Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Differentialtopologie (DE-588)4012255-4 gnd |
| subject_GND | (DE-588)4012255-4 (DE-588)1071861417 |
| title | Differential Topology |
| title_auth | Differential Topology |
| title_exact_search | Differential Topology |
| title_full | Differential Topology by Morris W. Hirsch |
| title_fullStr | Differential Topology by Morris W. Hirsch |
| title_full_unstemmed | Differential Topology by Morris W. Hirsch |
| title_short | Differential Topology |
| title_sort | differential topology |
| topic | Mathematics Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Differentialtopologie (DE-588)4012255-4 gnd |
| topic_facet | Mathematics Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Differentialtopologie Konferenzschrift 1976 Varenna |
| url | https://doi.org/10.1007/978-1-4684-9449-5 |
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