Algebraic methods in unstable homotopy theory:
The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which are needed in the presentation of results, proven by Cohen, Moore, and the author, on the exponents of homotopy groups. The author introduces various aspects of u...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2010
|
| Series: | New mathematical monographs
12 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which are needed in the presentation of results, proven by Cohen, Moore, and the author, on the exponents of homotopy groups. The author introduces various aspects of unstable homotopy theory, including: homotopy groups with coefficients; localization and completion; the Hopf invariants of Hilton, James, and Toda; Samelson products; homotopy Bockstein spectral sequences; graded Lie algebras; differential homological algebra; and the exponent theorems concerning the homotopy groups of spheres and Moore spaces. This book is suitable for a course in unstable homotopy theory, following a first course in homotopy theory. It is also a valuable reference for both experts and graduate students wishing to enter the field |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xix, 554 pages) |
| ISBN: | 9780511691638 |
| DOI: | 10.1017/CBO9780511691638 |
Staff View
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| 245 | 1 | 0 | |a Algebraic methods in unstable homotopy theory |c Joseph Neisendorfer |
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| 505 | 8 | 0 | |t Homotopy groups with coefficients |t A general theory of localization |t Fibre extensions of squares and the Peterson-Stein formula |t Hilton-Hopf invariants and the EHP sequence |t James-Hopf invariants and Toda-Hopf invariants |t Samelson products |t Bockstein spectral sequences |t Lie algebras and universal enveloping algebras |t Applications of graded Lie algebras |t Differential homological algebra |t Odd primary exponent theorems |t Differential homological algebra of classifying spaces |t Machine generated contents note: Preface; Introduction; 1. Homotopy groups with coefficients; 2. A general theory of localization; 3. Fibre extensions of squares and the Peterson-Stein formula; 4. Hilton-Hopf invariants and the EHP sequence; 5. James-Hopf invariants and Toda-Hopf invariants; 6. Samelson products; 7. Bockstein spectral sequences; 8. Lie algebras and universal enveloping algebras; 9. Applications of graded Lie algebras; 10. Differential homological algebra; 11. Odd primary exponent theorems; 12. Differential homological algebra of classifying spaces; Bibliography; Index |
| 520 | |a The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which are needed in the presentation of results, proven by Cohen, Moore, and the author, on the exponents of homotopy groups. The author introduces various aspects of unstable homotopy theory, including: homotopy groups with coefficients; localization and completion; the Hopf invariants of Hilton, James, and Toda; Samelson products; homotopy Bockstein spectral sequences; graded Lie algebras; differential homological algebra; and the exponent theorems concerning the homotopy groups of spheres and Moore spaces. This book is suitable for a course in unstable homotopy theory, following a first course in homotopy theory. It is also a valuable reference for both experts and graduate students wishing to enter the field | ||
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Record in the Search Index
| _version_ | 1804176884343242752 |
|---|---|
| any_adam_object | |
| author | Neisendorfer, Joseph 1945- |
| author_facet | Neisendorfer, Joseph 1945- |
| author_role | aut |
| author_sort | Neisendorfer, Joseph 1945- |
| author_variant | j n jn |
| building | Verbundindex |
| bvnumber | BV043941995 |
| classification_rvk | SK 300 SK 320 |
| collection | ZDB-20-CBO |
| contents | Homotopy groups with coefficients A general theory of localization Fibre extensions of squares and the Peterson-Stein formula Hilton-Hopf invariants and the EHP sequence James-Hopf invariants and Toda-Hopf invariants Samelson products Bockstein spectral sequences Lie algebras and universal enveloping algebras Applications of graded Lie algebras Differential homological algebra Odd primary exponent theorems Differential homological algebra of classifying spaces Machine generated contents note: Preface; Introduction; 1. Homotopy groups with coefficients; 2. A general theory of localization; 3. Fibre extensions of squares and the Peterson-Stein formula; 4. Hilton-Hopf invariants and the EHP sequence; 5. James-Hopf invariants and Toda-Hopf invariants; 6. Samelson products; 7. Bockstein spectral sequences; 8. Lie algebras and universal enveloping algebras; 9. Applications of graded Lie algebras; 10. Differential homological algebra; 11. Odd primary exponent theorems; 12. Differential homological algebra of classifying spaces; Bibliography; Index |
| ctrlnum | (ZDB-20-CBO)CR9780511691638 (OCoLC)839034162 (DE-599)BVBBV043941995 |
| 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/CBO9780511691638 |
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| id | DE-604.BV043941995 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511691638 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350965 |
| oclc_num | 839034162 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xix, 554 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | New mathematical monographs |
| spelling | Neisendorfer, Joseph 1945- Verfasser aut Algebraic methods in unstable homotopy theory Joseph Neisendorfer Cambridge Cambridge University Press 2010 1 online resource (xix, 554 pages) txt rdacontent c rdamedia cr rdacarrier New mathematical monographs 12 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Homotopy groups with coefficients A general theory of localization Fibre extensions of squares and the Peterson-Stein formula Hilton-Hopf invariants and the EHP sequence James-Hopf invariants and Toda-Hopf invariants Samelson products Bockstein spectral sequences Lie algebras and universal enveloping algebras Applications of graded Lie algebras Differential homological algebra Odd primary exponent theorems Differential homological algebra of classifying spaces Machine generated contents note: Preface; Introduction; 1. Homotopy groups with coefficients; 2. A general theory of localization; 3. Fibre extensions of squares and the Peterson-Stein formula; 4. Hilton-Hopf invariants and the EHP sequence; 5. James-Hopf invariants and Toda-Hopf invariants; 6. Samelson products; 7. Bockstein spectral sequences; 8. Lie algebras and universal enveloping algebras; 9. Applications of graded Lie algebras; 10. Differential homological algebra; 11. Odd primary exponent theorems; 12. Differential homological algebra of classifying spaces; Bibliography; Index The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which are needed in the presentation of results, proven by Cohen, Moore, and the author, on the exponents of homotopy groups. The author introduces various aspects of unstable homotopy theory, including: homotopy groups with coefficients; localization and completion; the Hopf invariants of Hilton, James, and Toda; Samelson products; homotopy Bockstein spectral sequences; graded Lie algebras; differential homological algebra; and the exponent theorems concerning the homotopy groups of spheres and Moore spaces. This book is suitable for a course in unstable homotopy theory, following a first course in homotopy theory. It is also a valuable reference for both experts and graduate students wishing to enter the field Homotopy theory Algebraic topology Algebraische Methode (DE-588)4141841-4 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 s Algebraische Methode (DE-588)4141841-4 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-76037-9 https://doi.org/10.1017/CBO9780511691638 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Neisendorfer, Joseph 1945- Algebraic methods in unstable homotopy theory Homotopy groups with coefficients A general theory of localization Fibre extensions of squares and the Peterson-Stein formula Hilton-Hopf invariants and the EHP sequence James-Hopf invariants and Toda-Hopf invariants Samelson products Bockstein spectral sequences Lie algebras and universal enveloping algebras Applications of graded Lie algebras Differential homological algebra Odd primary exponent theorems Differential homological algebra of classifying spaces Machine generated contents note: Preface; Introduction; 1. Homotopy groups with coefficients; 2. A general theory of localization; 3. Fibre extensions of squares and the Peterson-Stein formula; 4. Hilton-Hopf invariants and the EHP sequence; 5. James-Hopf invariants and Toda-Hopf invariants; 6. Samelson products; 7. Bockstein spectral sequences; 8. Lie algebras and universal enveloping algebras; 9. Applications of graded Lie algebras; 10. Differential homological algebra; 11. Odd primary exponent theorems; 12. Differential homological algebra of classifying spaces; Bibliography; Index Homotopy theory Algebraic topology Algebraische Methode (DE-588)4141841-4 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4141841-4 (DE-588)4128142-1 |
| title | Algebraic methods in unstable homotopy theory |
| title_alt | Homotopy groups with coefficients A general theory of localization Fibre extensions of squares and the Peterson-Stein formula Hilton-Hopf invariants and the EHP sequence James-Hopf invariants and Toda-Hopf invariants Samelson products Bockstein spectral sequences Lie algebras and universal enveloping algebras Applications of graded Lie algebras Differential homological algebra Odd primary exponent theorems Differential homological algebra of classifying spaces Machine generated contents note: Preface; Introduction; 1. Homotopy groups with coefficients; 2. A general theory of localization; 3. Fibre extensions of squares and the Peterson-Stein formula; 4. Hilton-Hopf invariants and the EHP sequence; 5. James-Hopf invariants and Toda-Hopf invariants; 6. Samelson products; 7. Bockstein spectral sequences; 8. Lie algebras and universal enveloping algebras; 9. Applications of graded Lie algebras; 10. Differential homological algebra; 11. Odd primary exponent theorems; 12. Differential homological algebra of classifying spaces; Bibliography; Index |
| title_auth | Algebraic methods in unstable homotopy theory |
| title_exact_search | Algebraic methods in unstable homotopy theory |
| title_full | Algebraic methods in unstable homotopy theory Joseph Neisendorfer |
| title_fullStr | Algebraic methods in unstable homotopy theory Joseph Neisendorfer |
| title_full_unstemmed | Algebraic methods in unstable homotopy theory Joseph Neisendorfer |
| title_short | Algebraic methods in unstable homotopy theory |
| title_sort | algebraic methods in unstable homotopy theory |
| topic | Homotopy theory Algebraic topology Algebraische Methode (DE-588)4141841-4 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Homotopy theory Algebraic topology Algebraische Methode Homotopietheorie |
| url | https://doi.org/10.1017/CBO9780511691638 |
| work_keys_str_mv | AT neisendorferjoseph algebraicmethodsinunstablehomotopytheory |