Rational homotopical models and uniqueness:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2000
|
| Series: | American Mathematical Society: Memoirs of the American Mathematical Society
682 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Volume 143, Number 682 (end of volume) |
| Physical Description: | XVIII, 149 S. |
| ISBN: | 0821819208 |
Staff View
MARC
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| 100 | 1 | |a Majewski, Martin |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Rational homotopical models and uniqueness |c Martin Majewski |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2000 | |
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| 490 | 1 | |a American Mathematical Society: Memoirs of the American Mathematical Society |v 682 | |
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| 502 | |a Zugl.: Berlin, Freie Univ., Diss., 1996 | ||
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
Abstract x
Keywords x
Preface xi
Introduction xiii
1. Homotopy Theory 1
1. Homotopical Categories 1
1. The axioms 1
2. Left homotopical categories 3
3. Homotopical subcategories 4
2. Fundamental Results 6
1. Lifting and extension 6
2. The derived category 7
3. Homotopical functors and their derived functors 8
4. The Adjoint Functor Theorem 9
3. COMONOIDS UP TO HOMOTOPY 11
1. ... as comonoids over the derived category 11
2. Derived tensor product 12
3. Generalizations 13
A. Examples of Homotopical Categories 15
1. Cofibration categories 15
2. Model categories 18
3. Spaces 20
4. Simplicial objects 21
2. Differential Algebra 25
1. Preliminaries 25
1. Chain complexes 25
2. DG (co)algebras 27
3. Tensor (co) algebras 29
2. Twisting Maps and the (Co)Bar Construction 30
1. Twisting maps and homotopies 30
2. The (co)bar construction 30
3. Compatibility with tensor product 32
4. Homological properties 32
3. Acyclic Models 33
1. Representable functors 33
2. The method of acyclic models 35
3. Duality 36
4. Acyclic model theorems for twisting maps 40
4. EZ-MORPHISMS 43
1. Extension of an EZ-morphism 43
2. A generalization 44
3. Properties of the extension 46
vii
viii Contents
B. Chain (Co)Functors 48
1. Monoidal categories 48
2. Normalization 49
3. Representable cofunctors for spaces 51
4. Cohomology theories 55
3. Complete Algebra 57
1. Complete Augmented Algebras 51
1. Ring systems 57
2. Complete modules 59
3. Complete augmented algebras and free groups 63
4. Rigidity 65
2. Complete Lie algebras and Complete Hopf Algebras 61
1. Complete Hopf algebras and the exponential mapping 61
2. The PBW-Theorem 69
3. Normal complete Hopf algebras 13
4. Rigidity 16
3. Complete Groups 77
1. Nilpotent groups 77
2. Complete groups 19
3. The Lazard - Mal cev correspondence 82
4. The Quillen functor 86
C. Filtered Modules 81
1. Filtered vs. cofiltered modules 81
2. Normal maps and exactness 89
3. Filtered tensor product 91
4. Complete Differential Algebra 94
4. Three Models for Spaces 97
1. The Cellular Model 91
1. The homotopical category of dg algebras 91
2. The homotopical category of dg Hopf algebras up to homotopy 99
3. The cobar-chain functor and the chain-loop functor 100
4. Compatibility with (tensor) products 101
5. The homotopy diagonals 102
2. The Sullivan Model 104
1. The homotopical category of commutative dg* algebras 104
2. The Sullivan cofunctor and Stokes map 106
3. Extension of Stokes map 108
4. Compatibility with (tensor) products 109
5. Dualization 110
6. The homotopy diagonals 113
3. The Quillen Model 115
1. The homotopical category of dg Lie algebras 115
2. The Quillen functor 116
3. Connection to the chain-loop functor 118
4. The group algebra of a free simplicial group 121
5. A proof of the Quillen equivalence 123
Contents i.x
4. Main Results 126
1. Summary 126
2. Anick s equivalence 127
3. Proof of the Baues - Lemaire conjecture 128
4. Rational equivalence 129
D. The Cellular Lie Algebra Model 130
1. A natural diagonal for the cobar-chain functor 130
2. A natural Hopf diagonal 133
3. The category of dg Lie algebras (over any ring) 134
4. Anick s theorems and naturality 139
Notations 145
Bibliography 147
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:38:02Z |
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| isbn | 0821819208 |
| language | English |
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| physical | XVIII, 149 S. |
| publishDate | 2000 |
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| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spelling | Majewski, Martin Verfasser aut Rational homotopical models and uniqueness Martin Majewski Providence, RI American Math. Soc. 2000 XVIII, 149 S. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Memoirs of the American Mathematical Society 682 Volume 143, Number 682 (end of volume) Zugl.: Berlin, Freie Univ., Diss., 1996 Homotopia larpcal Homotopie gtt Hopf-algebra's gtt Homotopy theory Hopf algebras Hopf-Algebra (DE-588)4160646-2 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Homotopietheorie (DE-588)4128142-1 s Hopf-Algebra (DE-588)4160646-2 s DE-604 American Mathematical Society: Memoirs of the American Mathematical Society 682 (DE-604)BV008000141 682 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008881167&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Majewski, Martin Rational homotopical models and uniqueness American Mathematical Society: Memoirs of the American Mathematical Society Homotopia larpcal Homotopie gtt Hopf-algebra's gtt Homotopy theory Hopf algebras Hopf-Algebra (DE-588)4160646-2 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4160646-2 (DE-588)4128142-1 (DE-588)4113937-9 |
| title | Rational homotopical models and uniqueness |
| title_auth | Rational homotopical models and uniqueness |
| title_exact_search | Rational homotopical models and uniqueness |
| title_full | Rational homotopical models and uniqueness Martin Majewski |
| title_fullStr | Rational homotopical models and uniqueness Martin Majewski |
| title_full_unstemmed | Rational homotopical models and uniqueness Martin Majewski |
| title_short | Rational homotopical models and uniqueness |
| title_sort | rational homotopical models and uniqueness |
| topic | Homotopia larpcal Homotopie gtt Hopf-algebra's gtt Homotopy theory Hopf algebras Hopf-Algebra (DE-588)4160646-2 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Homotopia Homotopie Hopf-algebra's Homotopy theory Hopf algebras Hopf-Algebra Homotopietheorie Hochschulschrift |
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| work_keys_str_mv | AT majewskimartin rationalhomotopicalmodelsanduniqueness |