Isomonodromic deformations and Frobenius manifolds: an introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer [u.a.]
2007
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 279 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9781848000537 1848000537 9781848000544 9782759800476 |
Internformat
MARC
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| 020 | |a 1848000537 |c Pb. : ca. EUR 42.75 (freier Pr.), ca. sfr 70.00 (freier Pr.) |9 1-8480-0053-7 | ||
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| 100 | 1 | |a Sabbah, Claude |d 1954- |e Verfasser |0 (DE-588)141260785 |4 aut | |
| 240 | 1 | 0 | |a Déformations isomonodromiques et variétés de Frobenius |
| 245 | 1 | 0 | |a Isomonodromic deformations and Frobenius manifolds |b an introduction |c Claude Sabbah |
| 264 | 1 | |a Berlin [u.a.] |b Springer [u.a.] |c 2007 | |
| 300 | |a XIV, 279 S. |b graph. Darst. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 650 | 4 | |a Frobenius manifolds | |
| 650 | 4 | |a Functions of several complex variables | |
| 650 | 4 | |a Holomorphic functions | |
| 650 | 4 | |a Isomonodromic deformation method | |
| 650 | 4 | |a Vector bundles | |
| 650 | 0 | 7 | |a Frobenius-Mannigfaltigkeit |0 (DE-588)4470001-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Deformation |g Mathematik |0 (DE-588)4011284-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Isomonodrome Deformation |0 (DE-588)4123454-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Isomonodrome Deformation |0 (DE-588)4123454-6 |D s |
| 689 | 0 | 1 | |a Frobenius-Mannigfaltigkeit |0 (DE-588)4470001-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Frobenius-Mannigfaltigkeit |0 (DE-588)4470001-5 |D s |
| 689 | 1 | 1 | |a Deformation |g Mathematik |0 (DE-588)4011284-6 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016373283 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804137456743743488 |
|---|---|
| adam_text | Contents
Prefece
........................................................
IX
Terminology and notation
.....................................XIII
0
The language of fibre bundles
............................ 1
1
Holoiiiorpliic functions on an open set of C
.............. 1
2
Complex analytic· manifolds
............................. 2
3
Holomorphie vector bundle1
............................. 5
4
Locally free .sheaves of ¿/^-modules
...................... 7
5
Nonabelian cohomology
................................ 10
6
Čech
cohomology
...................................... 14
7
Line bundles
.......................................... 16
8
Meromorphic bundles, lattices
........................... 17
9
Examples of holomorphie and meromorphic bundles
....... 19
10
Affine
varieties, analytization. algebraic differential forms
... 25
11
Holomorphie connections on a vector bundle
.............. 27
12
Holomorphie
integrable
connections and Higgs fields
....... 32
13
Geometry of the tangent bundle
......................... 37
14
Meromorphic connections
............................... 44
15
Locally constant sheaves
............................... 48
16
Integrable
deformations and isomonodromic deformations.
.. 53
17
Appendix: the language of categories
..................... 57
1 Holomorphie vector bundles on the Riemann sphere
..... 61
1
Cohomology of
С. С*
and
Ρ1
............................ 01
2
Line bundles on P1
....................................
G3
3
A finit
eness theorem and some consequences
.............. 68
4
Structure of vector bundles on P1
........................
G9
•5
Families of vector bundles on P1
......................... 70
VIII Contents
II The Riemann-Hilbert correspondence on a Riemann
surface
.................................................. 83
1
Statement of the problems
.............................. 83
2
Local study of regular singularities
....................... 85
3
Applications
.......................................... 97
4
Complements
.........................................100
5
Irregular singularities: local study
.......................102
6
The Riemann-Hilbert correspondence in the irregular case
. . 109
III Lattices
..................................................121
1
Lattices of (k, V)-vector spaces with regular singularity
.... 122
2
Lattices of (fe, V)-vector spaces with an irregular singularity
133
IV The Riemann-Hilbert problem and Birkhoff s problem
. . 145
1
The Riemann-Hilbert problem
..........................146
2
Meromorphic bundles with irreducible connection
..........152
3
Application to the Riemann-Hilbert problem
..............155
4
Complements on irreducibility
..........................158
5
Birkhoff s problem
.....................................159
V Fourier-Laplace duality
..................................167
1
Modules over the Weyl algebra
..........................168
2
Fourier transform
......................................176
3
Fourier transform and microlocalization
..................183
VI
Integrable
deformations of bundles with connection on
the Riemann sphere
.....................................191
1
The Riemann-Hilbert problem in a family
................192
2
Birkhoff s problem in a family
...........................200
3
Universal
integrable
deformation for Birkhoff s problem
.... 208
VII Saito
structures and Frobenius structures on a complex
analytic manifold
........................................223
1
Saito
structure on a manifold
...........................224
2
Frobenius structure on a manifold
.......................233
3
Infinitesimal period mapping
............................237
4
Examples
.............................................242
5
Frobenius-Saito structure associated to a singularity
.......254
References
.....................................................263
Index of Notation
.............................................273
Index
..........................................................275
|
| adam_txt |
Contents
Prefece
.
IX
Terminology and notation
.XIII
0
The language of fibre bundles
. 1
1
Holoiiiorpliic functions on an open set of C"
. 1
2
Complex analytic· manifolds
. 2
3
Holomorphie vector bundle1
. 5
4
Locally free .sheaves of ¿/^-modules
. 7
5
Nonabelian cohomology
. 10
6
Čech
cohomology
. 14
7
Line bundles
. 16
8
Meromorphic bundles, lattices
. 17
9
Examples of holomorphie and meromorphic bundles
. 19
10
Affine
varieties, analytization. algebraic differential forms
. 25
11
Holomorphie connections on a vector bundle
. 27
12
Holomorphie
integrable
connections and Higgs fields
. 32
13
Geometry of the tangent bundle
. 37
14
Meromorphic connections
. 44
15
Locally constant sheaves
. 48
16
Integrable
deformations and isomonodromic deformations.
. 53
17
Appendix: the language of categories
. 57
1 Holomorphie vector bundles on the Riemann sphere
. 61
1
Cohomology of
С. С*
and
Ρ1
. 01
2
Line bundles on P1
.
G3
3
A finit
eness theorem and some consequences
. 68
4
Structure of vector bundles on P1
.
G9
•5
Families of vector bundles on P1
. 70
VIII Contents
II The Riemann-Hilbert correspondence on a Riemann
surface
. 83
1
Statement of the problems
. 83
2
Local study of regular singularities
. 85
3
Applications
. 97
4
Complements
.100
5
Irregular singularities: local study
.102
6
The Riemann-Hilbert correspondence in the irregular case
. . 109
III Lattices
.121
1
Lattices of (k, V)-vector spaces with regular singularity
. 122
2
Lattices of (fe, V)-vector spaces with an irregular singularity
133
IV The Riemann-Hilbert problem and Birkhoff's problem
. . 145
1
The Riemann-Hilbert problem
.146
2
Meromorphic bundles with irreducible connection
.152
3
Application to the Riemann-Hilbert problem
.155
4
Complements on irreducibility
.158
5
Birkhoff's problem
.159
V Fourier-Laplace duality
.167
1
Modules over the Weyl algebra
.168
2
Fourier transform
.176
3
Fourier transform and microlocalization
.183
VI
Integrable
deformations of bundles with connection on
the Riemann sphere
.191
1
The Riemann-Hilbert problem in a family
.192
2
Birkhoff's problem in a family
.200
3
Universal
integrable
deformation for Birkhoff "s problem
. 208
VII Saito
structures and Frobenius structures on a complex
analytic manifold
.223
1
Saito
structure on a manifold
.224
2
Frobenius structure on a manifold
.233
3
Infinitesimal period mapping
.237
4
Examples
.242
5
Frobenius-Saito structure associated to a singularity
.254
References
.263
Index of Notation
.273
Index
.275 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Sabbah, Claude 1954- |
| author_GND | (DE-588)141260785 |
| author_facet | Sabbah, Claude 1954- |
| author_role | aut |
| author_sort | Sabbah, Claude 1954- |
| author_variant | c s cs |
| building | Verbundindex |
| bvnumber | BV023186825 |
| callnumber-first | Q - Science |
| callnumber-label | QA331 |
| callnumber-raw | QA331 |
| callnumber-search | QA331 |
| callnumber-sort | QA 3331 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 240 SK 500 SK 780 |
| ctrlnum | (OCoLC)255688719 (DE-599)DNB985199970 |
| dewey-full | 515.354 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.354 |
| dewey-search | 515.354 |
| dewey-sort | 3515.354 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV023186825 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:03:27Z |
| indexdate | 2024-07-09T21:12:35Z |
| institution | BVB |
| isbn | 9781848000537 1848000537 9781848000544 9782759800476 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016373283 |
| oclc_num | 255688719 |
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| owner | DE-355 DE-BY-UBR DE-703 DE-11 DE-19 DE-BY-UBM DE-384 |
| owner_facet | DE-355 DE-BY-UBR DE-703 DE-11 DE-19 DE-BY-UBM DE-384 |
| physical | XIV, 279 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer [u.a.] |
| record_format | marc |
| series2 | Universitext |
| spelling | Sabbah, Claude 1954- Verfasser (DE-588)141260785 aut Déformations isomonodromiques et variétés de Frobenius Isomonodromic deformations and Frobenius manifolds an introduction Claude Sabbah Berlin [u.a.] Springer [u.a.] 2007 XIV, 279 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Universitext Frobenius manifolds Functions of several complex variables Holomorphic functions Isomonodromic deformation method Vector bundles Frobenius-Mannigfaltigkeit (DE-588)4470001-5 gnd rswk-swf Deformation Mathematik (DE-588)4011284-6 gnd rswk-swf Isomonodrome Deformation (DE-588)4123454-6 gnd rswk-swf Isomonodrome Deformation (DE-588)4123454-6 s Frobenius-Mannigfaltigkeit (DE-588)4470001-5 s DE-604 Deformation Mathematik (DE-588)4011284-6 s 1\p DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016373283&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sabbah, Claude 1954- Isomonodromic deformations and Frobenius manifolds an introduction Frobenius manifolds Functions of several complex variables Holomorphic functions Isomonodromic deformation method Vector bundles Frobenius-Mannigfaltigkeit (DE-588)4470001-5 gnd Deformation Mathematik (DE-588)4011284-6 gnd Isomonodrome Deformation (DE-588)4123454-6 gnd |
| subject_GND | (DE-588)4470001-5 (DE-588)4011284-6 (DE-588)4123454-6 |
| title | Isomonodromic deformations and Frobenius manifolds an introduction |
| title_alt | Déformations isomonodromiques et variétés de Frobenius |
| title_auth | Isomonodromic deformations and Frobenius manifolds an introduction |
| title_exact_search | Isomonodromic deformations and Frobenius manifolds an introduction |
| title_exact_search_txtP | Isomonodromic deformations and Frobenius manifolds an introduction |
| title_full | Isomonodromic deformations and Frobenius manifolds an introduction Claude Sabbah |
| title_fullStr | Isomonodromic deformations and Frobenius manifolds an introduction Claude Sabbah |
| title_full_unstemmed | Isomonodromic deformations and Frobenius manifolds an introduction Claude Sabbah |
| title_short | Isomonodromic deformations and Frobenius manifolds |
| title_sort | isomonodromic deformations and frobenius manifolds an introduction |
| title_sub | an introduction |
| topic | Frobenius manifolds Functions of several complex variables Holomorphic functions Isomonodromic deformation method Vector bundles Frobenius-Mannigfaltigkeit (DE-588)4470001-5 gnd Deformation Mathematik (DE-588)4011284-6 gnd Isomonodrome Deformation (DE-588)4123454-6 gnd |
| topic_facet | Frobenius manifolds Functions of several complex variables Holomorphic functions Isomonodromic deformation method Vector bundles Frobenius-Mannigfaltigkeit Deformation Mathematik Isomonodrome Deformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016373283&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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