Holdings: Stable homotopy around the Arf-Kervaire invariant

Stable homotopy around the Arf-Kervaire invariant:

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Bibliographic Details
Main Author:	Snaith, Victor P. 1944- (Author)
Format:	Book
Language:	English
Published:	Basel [u.a.] Birkhäuser 2009
Series:	Progress in mathematics 273
Subjects:	Homotopietheorie - Invariante Homotopy theory Invariante Homotopietheorie
Online Access:	Inhaltsverzeichnis
Physical Description:	XIV, 239 S.
ISBN:	9783764399030

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MARC


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adam_text	CONTENTS PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII 1 ALGEBRAIC TOPOLOGY BACKGROUND 1.1 STABLE HOMOTOPY GROUPS OF SPHERES . . . . . . . . . . . . . . . . . . 2 1.3 THE CLASSICAL STABLE HOMOTOPY CATEGORY . . . . . . . . . . . . . . . . 7 1.4 THE CLASSICAL ADAMS SPECTRAL SEQUENCE . . . . . . . . . . . . . . . . 14 1.5 SNAITH SPLITTINGS AND THE KAHN-PRIDDY THEOREM . . . . . . . . . . . 15 1.7 HOMOLOGY OPERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.8 THE ARF-KERVAIRE INVARIANT ONE PROBLEM . . . . . . . . . . . . . . . 28 2 THE ARF-KERVAIRE INVARIANT VIA QX 2.1 THE STEENROD ANNIHILATED SUBMODULE . . . . . . . . . . . . . . . . . 34 2.2 THE ARF-KERVAIRE INVARIANT AND * * (* * BO ) . . . . . . . . . . . . . 40 2.3 APPLICATIONS TO THE ARF-KERVAIRE INVARIANT ONE PROBLEM . . . . . . . 44 3 THE UPPER TRIANGULAR TECHNOLOGY 3.2 THE ROLE OF THE UPPER TRIANGULAR GROUP . . . . . . . . . . . . . . . . 58 3.3 AN APPLICATION TO ALGEBRAIC K-THEORY . . . . . . . . . . . . . . . . . 62 4 A BRIEF GLIMPSE OF ALGEBRAIC K-THEORY 4.1 SIMPLICIAL SETS AND THEIR REALISATIONS . . . . . . . . . . . . . . . . . 66 4.2 QUILLENS HIGHER ALGEBRAIC K-THEORY . . . . . . . . . . . . . . . . . . 68 4.3 THE CORRESPONDENCE BETWEEN AFFINE SCHEMES AND COMMUTATIVE RINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.4 HENSELIAN RINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.5 MODULO M K-THEORY OF HENSELIAN PAIRS . . . . . . . . . . . . . . . . 75 4.6 THE UNIVERSAL HOMOTOPY CONSTRUCTION . . . . . . . . . . . . . . . . . 76 4.7 K-THEORY OF ARCHIMEDEAN FIELDS . . . . . . . . . . . . . . . . . . . . 83 4.8 COMMUTATIVE BANACH ALGEBRAS . . . . . . . . . . . . . . . . . . . . 88 4.9 THE CASE OF C ( X ) VIA EXCISION . . . . . . . . . . . . . . . . . . . . . 89 VI CONTENTS 5 THE MATRIX CORRESPONDING TO 1 * 3 5.1 THE FUNDAMENTAL RESULT OF UPPER TRIANGULAR TECHNOLOGY . . . . . . . 93 5.2 2-ADIC HOMOTOPY OF BU * BO . . . . . . . . . . . . . . . . . . . . . . 95 5.3 THE MATRIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.4 THE MATRIX RELOADED . . . . . . . . . . . . . . . . . . . . . . . . . . 110 5.5 APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 6 REAL PROJECTIVE SPACE 6.1 MU -THEORY AND KU -THEORY OF RP N . . . . . . . . . . . . . . . . . . 120 6.2 BP -THEORY OF RP N . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 6.3 APPLICATION TO THE WHITEHEAD PRODUCT [ * N ,* N ] . . . . . . . . . . . . 129 6.4 BO, BU AND BSPIN E-INVARIANTS . . . . . . . . . . . . . . . . . . . . . 132 6.5 MU * -E-INVARIANTS AND ARF-KERVAIRE INVARIANTS . . . . . . . . . . . . 137 7 HUREWICZ IMAGES, BP -THEORY AND THE ARF-KERVAIRE INVARIANT 7.1 J * AND J * * . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 7.2 J * -THEORY, JU * -THEORY AND THE ARF-KERVAIRE INVARIANT . . . . . . . . 147 8 UPPER TRIANGULAR TECHNOLOGY AND THE ARF-KERVAIRE INVARIANT 8.1 ADAMS OPERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 8.2 K-THEORY EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 8.3 THE UPPER TRIANGULAR TECHNOLOGY EXAMPLES . . . . . . . . . . . . . . 175 8.4 APPLICATIONS OF UPPER TRIANGULAR TECHNOLOGY . . . . . . . . . . . . . 184 9 FUTURISTIC AND CONTEMPORARY STABLE HOMOTOPY 9.1 A 1 -HOMOTOPY THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . 199 9.2 SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
any_adam_object	1
author	Snaith, Victor P. 1944-
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id	DE-604.BV035369257
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indexdate	2024-07-09T21:32:18Z
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isbn	9783764399030
language	English
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physical	XIV, 239 S.
publishDate	2009
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publisher	Birkhäuser
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series	Progress in mathematics
series2	Progress in mathematics
spelling	Snaith, Victor P. 1944- Verfasser (DE-588)108351882 aut Stable homotopy around the Arf-Kervaire invariant Victor P. Snaith Stable homotopy around the Arf Kervaire invariant Basel [u.a.] Birkhäuser 2009 XIV, 239 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 273 Homotopietheorie - Invariante Homotopy theory Invariante (DE-588)4128781-2 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 s Invariante (DE-588)4128781-2 s DE-604 Progress in mathematics 273 (DE-604)BV000004120 273 SWBplus Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017173168&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Snaith, Victor P. 1944- Stable homotopy around the Arf-Kervaire invariant Progress in mathematics Homotopietheorie - Invariante Homotopy theory Invariante (DE-588)4128781-2 gnd Homotopietheorie (DE-588)4128142-1 gnd
subject_GND	(DE-588)4128781-2 (DE-588)4128142-1
title	Stable homotopy around the Arf-Kervaire invariant
title_alt	Stable homotopy around the Arf Kervaire invariant
title_auth	Stable homotopy around the Arf-Kervaire invariant
title_exact_search	Stable homotopy around the Arf-Kervaire invariant
title_full	Stable homotopy around the Arf-Kervaire invariant Victor P. Snaith
title_fullStr	Stable homotopy around the Arf-Kervaire invariant Victor P. Snaith
title_full_unstemmed	Stable homotopy around the Arf-Kervaire invariant Victor P. Snaith
title_short	Stable homotopy around the Arf-Kervaire invariant
title_sort	stable homotopy around the arf kervaire invariant
topic	Homotopietheorie - Invariante Homotopy theory Invariante (DE-588)4128781-2 gnd Homotopietheorie (DE-588)4128142-1 gnd
topic_facet	Homotopietheorie - Invariante Homotopy theory Invariante Homotopietheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017173168&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000004120
work_keys_str_mv	AT snaithvictorp stablehomotopyaroundthearfkervaireinvariant

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