Lectures on homotopy theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
North-Holland
1992
|
| Schriftenreihe: | North-Holland mathematics studies
171 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | An expanded version of lectures given at the Scuola Matematica Interuniversitaria, in Perugia, during the summer of 1989 The central idea of the lecture course which gave birth to this book was to define the homotopy groups of a space and then give all the machinery needed to prove in detail that the nth homotopy group of the sphere Sn, for n greater than or equal to 1 is isomorphic to the group of the integers, that the lower homotopy groups of Sn are trivial and that the third homotopy group of S2 is also isomorphic to the group of the integers. All this was achieved by discussing H-spaces and CoH-spaces, fibrations and cofibrations (rather thoroughly), simplicial structures and the homotopy groups of maps. Later, the book was expanded to introduce CW-complexes and their homotopy groups, to construct a special class of CW-complexes (the Eilenberg-Mac Lane spaces) and to include a chapter devoted to the study of the action of the fundamental group on the higher homotopy groups and the study of fibrations in the context of a category in which the fibres are forced to live; the final material of that chapter is a comparison of various kinds of universal fibrations. Completing the book are two appendices on compactly generated spaces and the theory of colimits. The book does not require any prior knowledge of Algebraic Topology and only rudimentary concepts of Category Theory are necessary; however, the student is supposed to be well at ease with the main general theorems of Topology and have a reasonable mathematical maturity Includes bibliographical references (p. [285]-287) and index |
| Beschreibung: | 1 Online-Ressource (xii, 293 p.) |
| ISBN: | 9780444892386 0444892389 |
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| 100 | 1 | |a Piccinini, Renzo A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Lectures on homotopy theory |c Renzo A. Piccinini |
| 264 | 1 | |a Amsterdam |b North-Holland |c 1992 | |
| 300 | |a 1 Online-Ressource (xii, 293 p.) | ||
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| 490 | 0 | |a North-Holland mathematics studies |v 171 | |
| 500 | |a An expanded version of lectures given at the Scuola Matematica Interuniversitaria, in Perugia, during the summer of 1989 | ||
| 500 | |a The central idea of the lecture course which gave birth to this book was to define the homotopy groups of a space and then give all the machinery needed to prove in detail that the nth homotopy group of the sphere Sn, for n greater than or equal to 1 is isomorphic to the group of the integers, that the lower homotopy groups of Sn are trivial and that the third homotopy group of S2 is also isomorphic to the group of the integers. All this was achieved by discussing H-spaces and CoH-spaces, fibrations and cofibrations (rather thoroughly), simplicial structures and the homotopy groups of maps. Later, the book was expanded to introduce CW-complexes and their homotopy groups, to construct a special class of CW-complexes (the Eilenberg-Mac Lane spaces) and to include a chapter devoted to the study of the action of the fundamental group on the higher homotopy groups and the study of fibrations in the context of a category in which the fibres are forced to live; the final material of that chapter is a comparison of various kinds of universal fibrations. Completing the book are two appendices on compactly generated spaces and the theory of colimits. The book does not require any prior knowledge of Algebraic Topology and only rudimentary concepts of Category Theory are necessary; however, the student is supposed to be well at ease with the main general theorems of Topology and have a reasonable mathematical maturity | ||
| 500 | |a Includes bibliographical references (p. [285]-287) and index | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Piccinini, Renzo A. |
| author_facet | Piccinini, Renzo A. |
| author_role | aut |
| author_sort | Piccinini, Renzo A. |
| author_variant | r a p ra rap |
| building | Verbundindex |
| bvnumber | BV042317616 |
| collection | ZDB-33-ESD ZDB-33-EBS |
| ctrlnum | (ZDB-33-EBS)ocn316566728 (OCoLC)316566728 (DE-599)BVBBV042317616 |
| 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 |
| format | Electronic eBook |
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| id | DE-604.BV042317616 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:18:17Z |
| institution | BVB |
| isbn | 9780444892386 0444892389 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027754607 |
| oclc_num | 316566728 |
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| owner_facet | DE-1046 |
| physical | 1 Online-Ressource (xii, 293 p.) |
| psigel | ZDB-33-ESD ZDB-33-EBS FAW_PDA_ESD FLA_PDA_ESD |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | North-Holland |
| record_format | marc |
| series2 | North-Holland mathematics studies |
| spelling | Piccinini, Renzo A. Verfasser aut Lectures on homotopy theory Renzo A. Piccinini Amsterdam North-Holland 1992 1 Online-Ressource (xii, 293 p.) txt rdacontent c rdamedia cr rdacarrier North-Holland mathematics studies 171 An expanded version of lectures given at the Scuola Matematica Interuniversitaria, in Perugia, during the summer of 1989 The central idea of the lecture course which gave birth to this book was to define the homotopy groups of a space and then give all the machinery needed to prove in detail that the nth homotopy group of the sphere Sn, for n greater than or equal to 1 is isomorphic to the group of the integers, that the lower homotopy groups of Sn are trivial and that the third homotopy group of S2 is also isomorphic to the group of the integers. All this was achieved by discussing H-spaces and CoH-spaces, fibrations and cofibrations (rather thoroughly), simplicial structures and the homotopy groups of maps. Later, the book was expanded to introduce CW-complexes and their homotopy groups, to construct a special class of CW-complexes (the Eilenberg-Mac Lane spaces) and to include a chapter devoted to the study of the action of the fundamental group on the higher homotopy groups and the study of fibrations in the context of a category in which the fibres are forced to live; the final material of that chapter is a comparison of various kinds of universal fibrations. Completing the book are two appendices on compactly generated spaces and the theory of colimits. The book does not require any prior knowledge of Algebraic Topology and only rudimentary concepts of Category Theory are necessary; however, the student is supposed to be well at ease with the main general theorems of Topology and have a reasonable mathematical maturity Includes bibliographical references (p. [285]-287) and index Homotopie Homotopia larpcal Homotopie ram Homotopy theory fast Homotopy theory Homotopie (DE-588)4025803-8 gnd rswk-swf Homotopie (DE-588)4025803-8 s 1\p DE-604 http://www.sciencedirect.com/science/book/9780444892386 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Piccinini, Renzo A. Lectures on homotopy theory Homotopie Homotopia larpcal Homotopie ram Homotopy theory fast Homotopy theory Homotopie (DE-588)4025803-8 gnd |
| subject_GND | (DE-588)4025803-8 |
| title | Lectures on homotopy theory |
| title_auth | Lectures on homotopy theory |
| title_exact_search | Lectures on homotopy theory |
| title_full | Lectures on homotopy theory Renzo A. Piccinini |
| title_fullStr | Lectures on homotopy theory Renzo A. Piccinini |
| title_full_unstemmed | Lectures on homotopy theory Renzo A. Piccinini |
| title_short | Lectures on homotopy theory |
| title_sort | lectures on homotopy theory |
| topic | Homotopie Homotopia larpcal Homotopie ram Homotopy theory fast Homotopy theory Homotopie (DE-588)4025803-8 gnd |
| topic_facet | Homotopie Homotopia Homotopy theory |
| url | http://www.sciencedirect.com/science/book/9780444892386 |
| work_keys_str_mv | AT piccininirenzoa lecturesonhomotopytheory |