Noncommutative Maslov index and Eta-forms:
The author defines and proves a noncommutative generalization of a formula relating the Maslov index of a triple of Lagrangian subspaces of a symplectic vector space to eta-invariants associated to a pair of Lagrangian subspaces. The noncommutative Maslov index, defined for modules over a
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
2007
|
| Series: | Memoirs of the American Mathematical Society
887 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | The author defines and proves a noncommutative generalization of a formula relating the Maslov index of a triple of Lagrangian subspaces of a symplectic vector space to eta-invariants associated to a pair of Lagrangian subspaces. The noncommutative Maslov index, defined for modules over a |
| Item Description: | Volume 189, number 887 (last of four numbers.) Includes bibliographical references |
| Physical Description: | VI, 118 S. |
| ISBN: | 9780821839973 |
Staff View
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| 100 | 1 | |a Wahl, Charlotte |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Noncommutative Maslov index and Eta-forms |c Charlotte Wahl |
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 887 | |
| 500 | |a Volume 189, number 887 (last of four numbers.) | ||
| 500 | |a Includes bibliographical references | ||
| 520 | 3 | |a The author defines and proves a noncommutative generalization of a formula relating the Maslov index of a triple of Lagrangian subspaces of a symplectic vector space to eta-invariants associated to a pair of Lagrangian subspaces. The noncommutative Maslov index, defined for modules over a | |
| 650 | 7 | |a K-theorie |2 gtt | |
| 650 | 7 | |a Álgebras de operadores |2 larpcal | |
| 650 | 4 | |a Index theory (Mathematics) | |
| 650 | 4 | |a Maslov index | |
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Record in the Search Index
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| adam_text | Contents
Introduction 1
Summary 4
Notation and conventions 5
Chapter 1. Preliminaries 7
1.1. The geometric situation 7
1.2. The family index theorem 9
1.3. The algebra of differential forms 10
1.4. Lagrangian projections 16
Chapter 2. The Fredholm Operator and Its Index 21
2.1. The operator D on M 21
2.2. The operator Di on [0,1] 23
2.3. The operator Dz on the cylinder 27
2.4. The index of D+ 28
2.5. A perturbation with closed range 31
Chapter 3. Heat Semigroups and Kernels 33
3.1. Complex heat kernels 33
3.2. The heat semigroup on closed manifolds 38
3.3. The heat semigroup on [0,1] 40
3.4. The heat semigroup on the cylinder 44
3.5. The heat semigroup on M 49
Chapter 4. Superconnections and the Index Theorem 61
4.1. The superconnection A associated to Di 61
4.2. The superconnection associated to Dz 68
4.3. The superconnection A(p)t associated to D(p) 69
4.4. The index theorem and its proof 72
4.5. A gluing formula for 77 forms on S1 86
Chapter 5. Definitions and Techniques 91
5.1. Hilbert C* modules 91
5.2. Operators on spaces of vector valued functions 98
5.3. Projective systems and function spaces 105
5.4. Holomorphic semigroups 110
Bibliography 117
V
|
| adam_txt |
Contents
Introduction 1
Summary 4
Notation and conventions 5
Chapter 1. Preliminaries 7
1.1. The geometric situation 7
1.2. The family index theorem 9
1.3. The algebra of differential forms 10
1.4. Lagrangian projections 16
Chapter 2. The Fredholm Operator and Its Index 21
2.1. The operator D on M 21
2.2. The operator Di on [0,1] 23
2.3. The operator Dz on the cylinder 27
2.4. The index of D+ 28
2.5. A perturbation with closed range 31
Chapter 3. Heat Semigroups and Kernels 33
3.1. Complex heat kernels 33
3.2. The heat semigroup on closed manifolds 38
3.3. The heat semigroup on [0,1] 40
3.4. The heat semigroup on the cylinder 44
3.5. The heat semigroup on M 49
Chapter 4. Superconnections and the Index Theorem 61
4.1. The superconnection A\ associated to Di 61
4.2. The superconnection associated to Dz 68
4.3. The superconnection A(p)t associated to D(p) 69
4.4. The index theorem and its proof 72
4.5. A gluing formula for 77 forms on S1 86
Chapter 5. Definitions and Techniques 91
5.1. Hilbert C* modules 91
5.2. Operators on spaces of vector valued functions 98
5.3. Projective systems and function spaces 105
5.4. Holomorphic semigroups 110
Bibliography 117
V |
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| geographic_facet | C* Álgebras |
| id | DE-604.BV022751714 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:31:03Z |
| indexdate | 2024-07-09T21:05:17Z |
| institution | BVB |
| isbn | 9780821839973 |
| language | English |
| lccn | 2007060803 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015957432 |
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| physical | VI, 118 S. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
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| publisher | American Mathematical Society |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Wahl, Charlotte Verfasser aut Noncommutative Maslov index and Eta-forms Charlotte Wahl Providence, RI American Mathematical Society 2007 VI, 118 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 887 Volume 189, number 887 (last of four numbers.) Includes bibliographical references The author defines and proves a noncommutative generalization of a formula relating the Maslov index of a triple of Lagrangian subspaces of a symplectic vector space to eta-invariants associated to a pair of Lagrangian subspaces. The noncommutative Maslov index, defined for modules over a K-theorie gtt Álgebras de operadores larpcal Index theory (Mathematics) Maslov index K-theory K-Theorie (DE-588)4033335-8 gnd rswk-swf Indextheorie (DE-588)4161489-6 gnd rswk-swf Eta-Invariante (DE-588)4341718-8 gnd rswk-swf Maslov-Index (DE-588)4169023-0 gnd rswk-swf C* Álgebras larpcal K-Theorie (DE-588)4033335-8 s Maslov-Index (DE-588)4169023-0 s Indextheorie (DE-588)4161489-6 s Eta-Invariante (DE-588)4341718-8 s DE-604 Memoirs of the American Mathematical Society 887 (DE-604)BV008000141 887 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015957432&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wahl, Charlotte Noncommutative Maslov index and Eta-forms Memoirs of the American Mathematical Society K-theorie gtt Álgebras de operadores larpcal Index theory (Mathematics) Maslov index K-theory K-Theorie (DE-588)4033335-8 gnd Indextheorie (DE-588)4161489-6 gnd Eta-Invariante (DE-588)4341718-8 gnd Maslov-Index (DE-588)4169023-0 gnd |
| subject_GND | (DE-588)4033335-8 (DE-588)4161489-6 (DE-588)4341718-8 (DE-588)4169023-0 |
| title | Noncommutative Maslov index and Eta-forms |
| title_auth | Noncommutative Maslov index and Eta-forms |
| title_exact_search | Noncommutative Maslov index and Eta-forms |
| title_exact_search_txtP | Noncommutative Maslov index and Eta-forms |
| title_full | Noncommutative Maslov index and Eta-forms Charlotte Wahl |
| title_fullStr | Noncommutative Maslov index and Eta-forms Charlotte Wahl |
| title_full_unstemmed | Noncommutative Maslov index and Eta-forms Charlotte Wahl |
| title_short | Noncommutative Maslov index and Eta-forms |
| title_sort | noncommutative maslov index and eta forms |
| topic | K-theorie gtt Álgebras de operadores larpcal Index theory (Mathematics) Maslov index K-theory K-Theorie (DE-588)4033335-8 gnd Indextheorie (DE-588)4161489-6 gnd Eta-Invariante (DE-588)4341718-8 gnd Maslov-Index (DE-588)4169023-0 gnd |
| topic_facet | K-theorie Álgebras de operadores Index theory (Mathematics) Maslov index K-theory K-Theorie Indextheorie Eta-Invariante Maslov-Index C* Álgebras |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015957432&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT wahlcharlotte noncommutativemaslovindexandetaforms |