Involutions on Manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1971
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete
59 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book contains the results of work done during the years 1967-1970 on fixed-point-free involutions on manifolds, and is an enlarged version of the author's doctoral dissertation [54J written under the direction of Professor William Browder. The subject of fixed-paint-free involutions, as part of the subject of group actions on manifolds, has been an important source of problems, examples and ideas in topology for the last four decades, and receives renewed attention every time a new technical development suggests new questions and methods ([62, 8, 24, 63J). Here we consider mainly those properties of fixed-point-free involutions that can be best studied using the techniques of surgery on manifolds. This approach to the subject was initiated by Browder and Livesay. Special attention is given here to involutions of homotopy spheres, but even for this particular case, a more general theory is very useful. Two important related topics that we do not touch here are those of involutions with fixed points, and the relationship between fixed-point-free involutions and free Sl-actions. For these topics, the reader is referred to [23J, and to [33J, [61J, [82J, respectively. The two main problems we attack are those of classification of involutions, and the existence and uniqueness of invariant submanifolds with certain properties. As will be seen, these problems are closely related. If (T, l'n) is a fixed-point-free involution of a homotopy sphere l'n, the quotient l'n/Tis called a homotopy projective space |
| Beschreibung: | 1 Online-Ressource (X, 106 p) |
| ISBN: | 9783642650123 9783642650147 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-642-65012-3 |
Internformat
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Datensatz im Suchindex
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| author | López de Medrano, Santiago |
| author_facet | López de Medrano, Santiago |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-65012-3 |
| format | Electronic eBook |
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| spelling | López de Medrano, Santiago Verfasser aut Involutions on Manifolds by Santiago López de Medrano Berlin, Heidelberg Springer Berlin Heidelberg 1971 1 Online-Ressource (X, 106 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 59 0071-1136 This book contains the results of work done during the years 1967-1970 on fixed-point-free involutions on manifolds, and is an enlarged version of the author's doctoral dissertation [54J written under the direction of Professor William Browder. The subject of fixed-paint-free involutions, as part of the subject of group actions on manifolds, has been an important source of problems, examples and ideas in topology for the last four decades, and receives renewed attention every time a new technical development suggests new questions and methods ([62, 8, 24, 63J). Here we consider mainly those properties of fixed-point-free involutions that can be best studied using the techniques of surgery on manifolds. This approach to the subject was initiated by Browder and Livesay. Special attention is given here to involutions of homotopy spheres, but even for this particular case, a more general theory is very useful. Two important related topics that we do not touch here are those of involutions with fixed points, and the relationship between fixed-point-free involutions and free Sl-actions. For these topics, the reader is referred to [23J, and to [33J, [61J, [82J, respectively. The two main problems we attack are those of classification of involutions, and the existence and uniqueness of invariant submanifolds with certain properties. As will be seen, these problems are closely related. If (T, l'n) is a fixed-point-free involution of a homotopy sphere l'n, the quotient l'n/Tis called a homotopy projective space Mathematics Mathematics, general Mathematik Involution (DE-588)4162262-5 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Topologische Transformationsgruppe (DE-588)4738313-6 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Involution (DE-588)4162262-5 s Mannigfaltigkeit (DE-588)4037379-4 s 2\p DE-604 Topologische Transformationsgruppe (DE-588)4738313-6 s 3\p DE-604 https://doi.org/10.1007/978-3-642-65012-3 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | López de Medrano, Santiago Involutions on Manifolds Mathematics Mathematics, general Mathematik Involution (DE-588)4162262-5 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Topologische Transformationsgruppe (DE-588)4738313-6 gnd |
| subject_GND | (DE-588)4162262-5 (DE-588)4037379-4 (DE-588)4738313-6 (DE-588)4113937-9 |
| title | Involutions on Manifolds |
| title_auth | Involutions on Manifolds |
| title_exact_search | Involutions on Manifolds |
| title_full | Involutions on Manifolds by Santiago López de Medrano |
| title_fullStr | Involutions on Manifolds by Santiago López de Medrano |
| title_full_unstemmed | Involutions on Manifolds by Santiago López de Medrano |
| title_short | Involutions on Manifolds |
| title_sort | involutions on manifolds |
| topic | Mathematics Mathematics, general Mathematik Involution (DE-588)4162262-5 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Topologische Transformationsgruppe (DE-588)4738313-6 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Involution Mannigfaltigkeit Topologische Transformationsgruppe Hochschulschrift |
| url | https://doi.org/10.1007/978-3-642-65012-3 |
| work_keys_str_mv | AT lopezdemedranosantiago involutionsonmanifolds |