Algebraic homotopy:
This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in topology and algebra are discussed, including an introd...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1989
|
| Schriftenreihe: | Cambridge studies in advanced mathematics
15 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in topology and algebra are discussed, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful tools for homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group homotopy equivalences. Applications and examples of such computations are given, including when the fundamental group is non-trivial. Moreover, the deep connection between the homotopy classification problems and the cohomology theory of small categories is demonstrated. The prerequisites of the book are few: elementary topology and algebra. Consequently, this account will be valuable for non-specialists and experts alike. It is an important supplement to the standard presentations of algebraic topology, homotopy theory, category theory and homological algebra |
| Beschreibung: | 1 online resource (xix, 466 Seiten) |
| ISBN: | 9780511662522 |
| DOI: | 10.1017/CBO9780511662522 |
Internformat
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| 100 | 1 | |a Baues, Hans J. |d 1943- |e Verfasser |0 (DE-588)128430702 |4 aut | |
| 245 | 1 | 0 | |a Algebraic homotopy |c Hans Joachim Baues |
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| 490 | 0 | |a Cambridge studies in advanced mathematics |v 15 | |
| 520 | |a This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in topology and algebra are discussed, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful tools for homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group homotopy equivalences. Applications and examples of such computations are given, including when the fundamental group is non-trivial. Moreover, the deep connection between the homotopy classification problems and the cohomology theory of small categories is demonstrated. The prerequisites of the book are few: elementary topology and algebra. Consequently, this account will be valuable for non-specialists and experts alike. It is an important supplement to the standard presentations of algebraic topology, homotopy theory, category theory and homological algebra | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Baues, Hans J. 1943- |
| author_GND | (DE-588)128430702 |
| author_facet | Baues, Hans J. 1943- |
| author_role | aut |
| author_sort | Baues, Hans J. 1943- |
| author_variant | h j b hj hjb |
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| bvnumber | BV043942153 |
| classification_rvk | SK 300 SK 320 |
| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9780511662522 (OCoLC)849791625 (DE-599)BVBBV043942153 |
| dewey-full | 514/.24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.24 |
| dewey-search | 514/.24 |
| dewey-sort | 3514 224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511662522 |
| format | Electronic eBook |
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| id | DE-604.BV043942153 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511662522 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351123 |
| oclc_num | 849791625 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 online resource (xix, 466 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Cambridge University Press |
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| series2 | Cambridge studies in advanced mathematics |
| spelling | Baues, Hans J. 1943- Verfasser (DE-588)128430702 aut Algebraic homotopy Hans Joachim Baues Cambridge Cambridge University Press 1989 1 online resource (xix, 466 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 15 This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in topology and algebra are discussed, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful tools for homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group homotopy equivalences. Applications and examples of such computations are given, including when the fundamental group is non-trivial. Moreover, the deep connection between the homotopy classification problems and the cohomology theory of small categories is demonstrated. The prerequisites of the book are few: elementary topology and algebra. Consequently, this account will be valuable for non-specialists and experts alike. It is an important supplement to the standard presentations of algebraic topology, homotopy theory, category theory and homological algebra Homotopy theory Categories (Mathematics) Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-33376-4 Erscheint auch als Druck-Ausgabe 978-0-521-05531-4 https://doi.org/10.1017/CBO9780511662522 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Baues, Hans J. 1943- Algebraic homotopy Homotopy theory Categories (Mathematics) Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4128142-1 |
| title | Algebraic homotopy |
| title_auth | Algebraic homotopy |
| title_exact_search | Algebraic homotopy |
| title_full | Algebraic homotopy Hans Joachim Baues |
| title_fullStr | Algebraic homotopy Hans Joachim Baues |
| title_full_unstemmed | Algebraic homotopy Hans Joachim Baues |
| title_short | Algebraic homotopy |
| title_sort | algebraic homotopy |
| topic | Homotopy theory Categories (Mathematics) Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Homotopy theory Categories (Mathematics) Homotopietheorie |
| url | https://doi.org/10.1017/CBO9780511662522 |
| work_keys_str_mv | AT baueshansj algebraichomotopy |