ZZ/2, homotopy theory /:
This account is a study of twofold symmetry in algebraic topology. The author discusses specifically the antipodal involution of a real vector bundle - multiplication by - I in each fibre; doubling and squaring operations; the symmetry of bilinear forms and Hermitian K-theory. In spite of its title,...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [England] ; New York :
Cambridge University Press,
1980.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
44. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This account is a study of twofold symmetry in algebraic topology. The author discusses specifically the antipodal involution of a real vector bundle - multiplication by - I in each fibre; doubling and squaring operations; the symmetry of bilinear forms and Hermitian K-theory. In spite of its title, this is not a treatise on equivariant topology; rather it is the language in which to describe the symmetry. Familiarity with the basic concepts of algebraic topology (homotopy, stable homotopy, homology, K-theory, the Pontrjagin--Thom transfer construction) is assumed. Detailed proofs are not given (the expert reader will be able to supply them when necessary) yet nowhere is credibility lost. Thus the approach is elementary enough to provide an introduction to the subject suitable for graduate students although research workers will find here much of interest. |
| Beschreibung: | Based on the author's thesis, Oxford. |
| Beschreibung: | 1 online resource (128 pages) |
| Bibliographie: | Includes bibliographical references (pages 121-126) and index. |
| ISBN: | 9781107361065 1107361060 9780511662690 0511662696 |
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| 520 | |a This account is a study of twofold symmetry in algebraic topology. The author discusses specifically the antipodal involution of a real vector bundle - multiplication by - I in each fibre; doubling and squaring operations; the symmetry of bilinear forms and Hermitian K-theory. In spite of its title, this is not a treatise on equivariant topology; rather it is the language in which to describe the symmetry. Familiarity with the basic concepts of algebraic topology (homotopy, stable homotopy, homology, K-theory, the Pontrjagin--Thom transfer construction) is assumed. Detailed proofs are not given (the expert reader will be able to supply them when necessary) yet nowhere is credibility lost. Thus the approach is elementary enough to provide an introduction to the subject suitable for graduate students although research workers will find here much of interest. | ||
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| author | Crabb, M. C. (Michael Charles) |
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| contents | Cover; Title; Copyright; Contents; Acknowledgments; 1. Introduction; 2. The Euler class and obstruction theory; 3. Spherical fibrations; 4. Stable cohomotopy; 5. Framed manifolds; 6. K-theory; 7. The image of J; 8. The Euler characteristic; 9. Topological Hermitian K-theory; 10. Algebraic Hermitian K-theory; B. Appendix: On the Hermitian J-homomorphism; Bibliography; Index |
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| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:17Z |
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| isbn | 9781107361065 1107361060 9780511662690 0511662696 |
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| spelling | Crabb, M. C. (Michael Charles) https://id.oclc.org/worldcat/entity/E39PCjD3yGbJKkqjhtwBpyvrFX ZZ/2, homotopy theory / M.C. Crabb. Cambridge [England] ; New York : Cambridge University Press, 1980. 1 online resource (128 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 44 Based on the author's thesis, Oxford. Includes bibliographical references (pages 121-126) and index. Print version record. This account is a study of twofold symmetry in algebraic topology. The author discusses specifically the antipodal involution of a real vector bundle - multiplication by - I in each fibre; doubling and squaring operations; the symmetry of bilinear forms and Hermitian K-theory. In spite of its title, this is not a treatise on equivariant topology; rather it is the language in which to describe the symmetry. Familiarity with the basic concepts of algebraic topology (homotopy, stable homotopy, homology, K-theory, the Pontrjagin--Thom transfer construction) is assumed. Detailed proofs are not given (the expert reader will be able to supply them when necessary) yet nowhere is credibility lost. Thus the approach is elementary enough to provide an introduction to the subject suitable for graduate students although research workers will find here much of interest. Cover; Title; Copyright; Contents; Acknowledgments; 1. Introduction; 2. The Euler class and obstruction theory; 3. Spherical fibrations; 4. Stable cohomotopy; 5. Framed manifolds; 6. K-theory; 7. The image of J; 8. The Euler characteristic; 9. Topological Hermitian K-theory; 10. Algebraic Hermitian K-theory; B. Appendix: On the Hermitian J-homomorphism; Bibliography; Index Homotopy theory. http://id.loc.gov/authorities/subjects/sh85061803 Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Symmetry. http://id.loc.gov/authorities/subjects/sh85131440 Homotopie. Théorie des groupes. Symétrie. MATHEMATICS Topology. bisacsh Group theory fast Homotopy theory fast Symmetry fast Homotopie gnd http://d-nb.info/gnd/4025803-8 Homotopie. gtt has work: ZZ/2, homotopy theory (Text) https://id.oclc.org/worldcat/entity/E39PCGBGVqCVV6JwhxWC6GVbv3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Crabb, M.C. (Michael Charles). ZZ/2, homotopy theory. Cambridge [Eng.] ; New York : Cambridge University Press, 1980 0521280516 (DLC) 80040703 (OCoLC)6627386 London Mathematical Society lecture note series ; 44. FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552505 Volltext |
| spellingShingle | Crabb, M. C. (Michael Charles) ZZ/2, homotopy theory / London Mathematical Society lecture note series ; Cover; Title; Copyright; Contents; Acknowledgments; 1. Introduction; 2. The Euler class and obstruction theory; 3. Spherical fibrations; 4. Stable cohomotopy; 5. Framed manifolds; 6. K-theory; 7. The image of J; 8. The Euler characteristic; 9. Topological Hermitian K-theory; 10. Algebraic Hermitian K-theory; B. Appendix: On the Hermitian J-homomorphism; Bibliography; Index Homotopy theory. http://id.loc.gov/authorities/subjects/sh85061803 Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Symmetry. http://id.loc.gov/authorities/subjects/sh85131440 Homotopie. Théorie des groupes. Symétrie. MATHEMATICS Topology. bisacsh Group theory fast Homotopy theory fast Symmetry fast Homotopie gnd http://d-nb.info/gnd/4025803-8 Homotopie. gtt |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85061803 http://id.loc.gov/authorities/subjects/sh85057512 http://id.loc.gov/authorities/subjects/sh85131440 http://d-nb.info/gnd/4025803-8 |
| title | ZZ/2, homotopy theory / |
| title_auth | ZZ/2, homotopy theory / |
| title_exact_search | ZZ/2, homotopy theory / |
| title_full | ZZ/2, homotopy theory / M.C. Crabb. |
| title_fullStr | ZZ/2, homotopy theory / M.C. Crabb. |
| title_full_unstemmed | ZZ/2, homotopy theory / M.C. Crabb. |
| title_short | ZZ/2, homotopy theory / |
| title_sort | zz 2 homotopy theory |
| topic | Homotopy theory. http://id.loc.gov/authorities/subjects/sh85061803 Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Symmetry. http://id.loc.gov/authorities/subjects/sh85131440 Homotopie. Théorie des groupes. Symétrie. MATHEMATICS Topology. bisacsh Group theory fast Homotopy theory fast Symmetry fast Homotopie gnd http://d-nb.info/gnd/4025803-8 Homotopie. gtt |
| topic_facet | Homotopy theory. Group theory. Symmetry. Homotopie. Théorie des groupes. Symétrie. MATHEMATICS Topology. Group theory Homotopy theory Symmetry Homotopie |
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