Brackets in the Pontryagin algebras of manifolds:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Paris
Société Mathématique de France
[2017]
|
| Series: | Mémoires de la Société Mathématique de France. Nouvelle série
numéro 154 |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | 138 Seiten Illustrationen |
| ISBN: | 9782856298763 2856298761 |
Staff View
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| 245 | 1 | 0 | |a Brackets in the Pontryagin algebras of manifolds |c Gwénaël Massuyeau, Vladimir Turaev |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
i
Introduction ................................................................ 7
1. Algebras, brackets, and bibrackets ...................................... 13
1.1. Algebras and brackets .............................................. 13
1.2. Bibrackets ......................................................... 16
1.3. Equivariance ....................................................... 21
1.4. The associated pairing and the trace................................ 23
2. Bibrackets in unital algebras and in categories ......................... 27
2.1. Bibrackets in unital algebras ...................................... 27
2.2. Bibrackets in categories ........................................... 29
2.3. Bibrackets in Hopf categories ...................................... 31
2.4. Hamiltonian reduction of bibrackets ................................ 39
3. Face homology ........................................................... 43
3.1. Manifolds with faces and partitions ................................ 43
3.2. Polychains, polycycles, and face homology .......................... 46
3.3. Face homology versus singular homology ............................. 53
3.4. Smooth polychains .................................................. 63
4. Operations on polychains ................. ..............................69
4.1. Transversality in path spaces ...................................... 69
4.2. Intersection of polychains ......................................... 74
4.3. The operation T .................................................... 78
4.4. The operation T .................................................... 87
5. The intersection bibracket .............................................. 93
5.1. Construction of the intersection bibracket ......................... 93
5.2. The Jacobi identity ................................................ 97
5.3. Computations and examples ..........................................110
6
CONTENTS
6. Properties of the intersection bibracket ...
6.1. The scalar intersection form ...........
6.2. The reducibility .......................
6.3. The string bracket .....................
6.4. Moment maps and Hamiltonian reduction
Bibliography ..................................
Index .........................................
154
MÉMOIRES DE LA SME
A fundamental geometric object derived from an arbitrary topological space M
with a marked point ★ is the space of loops in M based at ★. The Pontryagin
algebra A of (M, ★) is the singular homology of this loop space with the graded
algebra structure induced by the standard multiplication of loops. When M is
a smooth oriented manifold with boundary and ★ is chosen on 9A/, we define
an “intersection” operation A® A — A g A. We prove that this operation is
a double bracket in the sense of Michel Van den Bergh satisfying a version of
the Jacobi identity. We show that our double bracket induces Gerstenhaber
brackets in the representation algebras of A. These results extend our previous
work on surfaces, where A is the group algebra of the fundamental group of
a surface and the Gerstenhaber brackets in question are the usual Poisson
brackets on the moduli spaces of representations of such a group. The present
work is inspired by the results of William Goldman on surfaces and by the
ideas of string topology due to Moira Chas and Dennis Sullivan.
Société
Mathématique
de France
ISBN 978-2-85629-876-3
imprimerie Sepec - o 1960 Péronnas - France
Dépôt légal : avril 2018 - N 0 N04615180303
ISSN 0249-633-X
|
| any_adam_object | 1 |
| author | Massuyeau, Gwénaël Turaev, Vladimir G. 1954- |
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| author_sort | Massuyeau, Gwénaël |
| author_variant | g m gm v g t vg vgt |
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| id | DE-604.BV044981021 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:06:18Z |
| institution | BVB |
| isbn | 9782856298763 2856298761 |
| language | English |
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| physical | 138 Seiten Illustrationen |
| publishDate | 2017 |
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| series | Mémoires de la Société Mathématique de France. Nouvelle série |
| series2 | Mémoires de la Société Mathématique de France. Nouvelle série |
| spelling | Massuyeau, Gwénaël Verfasser aut Brackets in the Pontryagin algebras of manifolds Gwénaël Massuyeau, Vladimir Turaev Paris Société Mathématique de France [2017] 2017 138 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Mémoires de la Société Mathématique de France. Nouvelle série numéro 154 Turaev, Vladimir G. 1954- (DE-588)122717791 aut Mémoires de la Société Mathématique de France. Nouvelle série numéro 154 (DE-604)BV000000921 154 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030373400&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030373400&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Massuyeau, Gwénaël Turaev, Vladimir G. 1954- Brackets in the Pontryagin algebras of manifolds Mémoires de la Société Mathématique de France. Nouvelle série |
| title | Brackets in the Pontryagin algebras of manifolds |
| title_auth | Brackets in the Pontryagin algebras of manifolds |
| title_exact_search | Brackets in the Pontryagin algebras of manifolds |
| title_full | Brackets in the Pontryagin algebras of manifolds Gwénaël Massuyeau, Vladimir Turaev |
| title_fullStr | Brackets in the Pontryagin algebras of manifolds Gwénaël Massuyeau, Vladimir Turaev |
| title_full_unstemmed | Brackets in the Pontryagin algebras of manifolds Gwénaël Massuyeau, Vladimir Turaev |
| title_short | Brackets in the Pontryagin algebras of manifolds |
| title_sort | brackets in the pontryagin algebras of manifolds |
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