Fibrewise Homotopy Theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
London
Springer London
1998
|
| Schriftenreihe: | Springer Monographs in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Topology occupies a central position in the mathematics of today. One of the most useful ideas to be introduced in the past sixty years is the concept of fibre bundle, which provides an appropriate framework for studying differential geometry and much else. Fibre bundles are examples of the kind of structures studied in fibrewise topology. Just as homotopy theory arises from topology, so fibrewise homotopy the ory arises from fibrewise topology. In this monograph we provide an overview of fibrewise homotopy theory as it stands at present. It is hoped that this may stimulate further research. The literature on the subject is already quite extensive but clearly there is a great deal more to be done. Efforts have been made to develop general theories of which ordinary homotopy theory, equivariant homotopy theory, fibrewise homotopy theory and so forth will be special cases. For example, Baues [7] and, more recently, Dwyer and Spalinski [53], have presented such general theories, derived from an earlier theory of Quillen, but none of these seem to provide quite the right framework for our purposes. We have preferred, in this monograph, to develop fibre wise homotopy theory more or less ab initio, assuming only a basic knowledge of ordinary homotopy theory, at least in the early sections, but our aim has been to keep the exposition reasonably self-contained |
| Beschreibung: | 1 Online-Ressource (VIII, 341p) |
| ISBN: | 9781447112655 9781447112679 |
| ISSN: | 1439-7382 |
| DOI: | 10.1007/978-1-4471-1265-5 |
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| 500 | |a Topology occupies a central position in the mathematics of today. One of the most useful ideas to be introduced in the past sixty years is the concept of fibre bundle, which provides an appropriate framework for studying differential geometry and much else. Fibre bundles are examples of the kind of structures studied in fibrewise topology. Just as homotopy theory arises from topology, so fibrewise homotopy the ory arises from fibrewise topology. In this monograph we provide an overview of fibrewise homotopy theory as it stands at present. It is hoped that this may stimulate further research. The literature on the subject is already quite extensive but clearly there is a great deal more to be done. Efforts have been made to develop general theories of which ordinary homotopy theory, equivariant homotopy theory, fibrewise homotopy theory and so forth will be special cases. For example, Baues [7] and, more recently, Dwyer and Spalinski [53], have presented such general theories, derived from an earlier theory of Quillen, but none of these seem to provide quite the right framework for our purposes. We have preferred, in this monograph, to develop fibre wise homotopy theory more or less ab initio, assuming only a basic knowledge of ordinary homotopy theory, at least in the early sections, but our aim has been to keep the exposition reasonably self-contained | ||
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Datensatz im Suchindex
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| author | Crabb, Michael Charles |
| author_facet | Crabb, Michael Charles |
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| author_sort | Crabb, Michael Charles |
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| bvnumber | BV042419373 |
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| ctrlnum | (OCoLC)863784921 (DE-599)BVBBV042419373 |
| dewey-full | 514 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514 |
| dewey-search | 514 |
| dewey-sort | 3514 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4471-1265-5 |
| format | Electronic eBook |
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| id | DE-604.BV042419373 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9781447112655 9781447112679 |
| issn | 1439-7382 |
| language | English |
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| spelling | Crabb, Michael Charles Verfasser aut Fibrewise Homotopy Theory by Michael Charles Crabb, Ioan Mackenzie James London Springer London 1998 1 Online-Ressource (VIII, 341p) txt rdacontent c rdamedia cr rdacarrier Springer Monographs in Mathematics 1439-7382 Topology occupies a central position in the mathematics of today. One of the most useful ideas to be introduced in the past sixty years is the concept of fibre bundle, which provides an appropriate framework for studying differential geometry and much else. Fibre bundles are examples of the kind of structures studied in fibrewise topology. Just as homotopy theory arises from topology, so fibrewise homotopy the ory arises from fibrewise topology. In this monograph we provide an overview of fibrewise homotopy theory as it stands at present. It is hoped that this may stimulate further research. The literature on the subject is already quite extensive but clearly there is a great deal more to be done. Efforts have been made to develop general theories of which ordinary homotopy theory, equivariant homotopy theory, fibrewise homotopy theory and so forth will be special cases. For example, Baues [7] and, more recently, Dwyer and Spalinski [53], have presented such general theories, derived from an earlier theory of Quillen, but none of these seem to provide quite the right framework for our purposes. We have preferred, in this monograph, to develop fibre wise homotopy theory more or less ab initio, assuming only a basic knowledge of ordinary homotopy theory, at least in the early sections, but our aim has been to keep the exposition reasonably self-contained Mathematics Topology Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Faserbündel (DE-588)4135582-9 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 s Faserbündel (DE-588)4135582-9 s 1\p DE-604 James, Ioan Mackenzie Sonstige oth https://doi.org/10.1007/978-1-4471-1265-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Crabb, Michael Charles Fibrewise Homotopy Theory Mathematics Topology Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Homotopietheorie (DE-588)4128142-1 gnd Faserbündel (DE-588)4135582-9 gnd |
| subject_GND | (DE-588)4128142-1 (DE-588)4135582-9 |
| title | Fibrewise Homotopy Theory |
| title_auth | Fibrewise Homotopy Theory |
| title_exact_search | Fibrewise Homotopy Theory |
| title_full | Fibrewise Homotopy Theory by Michael Charles Crabb, Ioan Mackenzie James |
| title_fullStr | Fibrewise Homotopy Theory by Michael Charles Crabb, Ioan Mackenzie James |
| title_full_unstemmed | Fibrewise Homotopy Theory by Michael Charles Crabb, Ioan Mackenzie James |
| title_short | Fibrewise Homotopy Theory |
| title_sort | fibrewise homotopy theory |
| topic | Mathematics Topology Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Homotopietheorie (DE-588)4128142-1 gnd Faserbündel (DE-588)4135582-9 gnd |
| topic_facet | Mathematics Topology Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Homotopietheorie Faserbündel |
| url | https://doi.org/10.1007/978-1-4471-1265-5 |
| work_keys_str_mv | AT crabbmichaelcharles fibrewisehomotopytheory AT jamesioanmackenzie fibrewisehomotopytheory |