Holomorphic families of immersions and higher analytic torsion forms:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
[Paris]
Soc. Math. de France
1997
|
| Series: | Astérisque
244 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 275 S. graph. Darst. |
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Record in the Search Index
| _version_ | 1804126590636916738 |
|---|---|
| adam_text | 244 ASTERISQUE 1997 HOLOMORPHIC FAMILIES OF IMMERSIONS AND HIGHER
ANALYTIC TORSION FORMS JEAN-MICHEL BISMUT SOCIETE MATHEMATIQUE DE FRANCE
PUBLIE AVEC LE CONCOURS DU CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE
CONTENTS INTRODUCTION 1 1 FAMILIES OF IMMERSIONS AND CONNECTIONS ON THE
RELATIVE TANGENT BUNDLE 13 1.1 A CANONICAL CONNECTION ON THE RELATIVE
TANGENT BUNDLE OF A FIBRATION 13 1.2 AN IDENTITY ON THE CONNECTION ON
THE RELATIVE TANGENT BUNDLE . . . . 15 1.3 FAMILIES OF IMMERSIONS AND
THE CORRESPONDING CONNECTIONS ON THE RELATIVE TANGENT BUNDLES 16 2
KAHLER FIBRATIONS, HIGHER ANALYTIC TORSION FORMS AND ANOMALY FORMU- LAS
23 2.1 KAHLER FIBRATIONS 23 2.2 COMPLEX HERMITIAN VECTOR SPACES AND
CLIFFORD ALGEBRAS 26 2.3 THE LEVI-CIVITA SUPERCONNECTION OF THE
FIBRATION . . . . 27 2.4 SUPERCONNECTION FORMS AND TRANSGRESSION
FORMULAS 29 2.5 THE ASYMPTOTICS OF THE SUPERCONNECTION FORMS AS U ** 0
30 2.6 THE ASYMPTOTICS OF THE SUPERCONNECTION FORMS ASU- +OO 31 2.7
HIGHER ANALYTIC TORSION FORMS 32 2.8 ANOMALY FORMULAS FOR THE ANALYTIC
TORSION FORMS 33 3 KAHLER FIBRATIONS, RESOLUTIONS, AND BOTT-CHERN
CURRENTS 35 3.1 A FAMILY OF DOUBLE COMPLEXES 35 3.2 THE ANALYTIC TORSION
FORMS OF THE DOUBLE COMPLEX 37 3.3 ASSUMPTIONS ON THE METRICS ON , R
40 3.4 A BOTT-CHERN CURRENT 41 4 AN IDENTITY ON TWO PARAMETERS
DIFFERENTIAL FORMS 43 4.1 A BASIC IDENTITY OF DIFFERENTIAL FORMS 43 4.2
A CHANGE OF COORDINATES 46 SOCIETE MATHEMATIQUE DE FRANCE IV CONTENTS
4.3 A CONTOUR INTEGRAL 47 4.4 SOME ELEMENTARY IDENTITIES 48 5 THE
ANALYTIC TORSION FORMS OF A SHORT EXACT SEQUENCE 51 5.1 SHORT EXACT
SEQUENCES ARID SUPERCONNECTIONS 51 5.2 THE CONJUGATE SUPERCONNECTIONS ^U
AND 9) U 54 5.3 GENERALIZED SUPERTRACES 55 5.4 TRANSGRESSION FORMULAS
AND CONVERGENCE OF GENERALIZED SUPERTRACES . 56 5.5 GENERALIZED ANALYTIC
TORSION FORMS 56 5.6 EVALUATION OF THE GENERALIZED ANALYTIC TORSION
FORMS 57 5.7 EQUIVARIANT GENERALIZED ANALYTIC TORSION FORMS 58 5.8 SOME
IDENTITIES ON GENERALIZED SUPERTRACES 60 5.9 A CONJUGATION FORMULA . .-
67 6 A PROOF OF THEOREM 0.1 , 69 6.1 THE MAIN THEOREM 70 6.2 A RESCALED
METRIC ON E . . 71 6.3 THE LEFT-HAND SIDE OF (4.26): SEVEN INTERMEDIATE
RESULTS 72 6.4 THE ASYMPTOTICS OF THE L S 74 THE TERM 7? 75 THE TERM 1$
7 7 THE TERM 1$ 79 THE TERM 1% 80 6.5 THE DIVERGENCES OF THE LEFT-HAND
SIDE OF (4.26) . . . 83 6.6 THE-RIGHT-HAND SIDE OF (4.26): FIVE
INTERMEDIATE RESULTS 84 6.7 THE ASYMPTOTICS OF THE RIGHT-HAND SIDE OF
(4.26) 88 6.8 MATCHING THE DIVERGENCES 105 6.9 AN IDENTITY ON BOTT-CHERN
CLASSES AND BOTT-CHERN CURRENTS 107 6.10 PROOF OF THEOREM 6.2 108 7 A
NEW HORIZONTAL BUNDLE ON V AND THE CONJUGATE SUPERCONNECTION A UYT 109
7.1 A FORMULA FOR D X AND D Y 110 7.2 THE CANONICAL EXACT SEQUENCE ON W
110 7.3 A COORDINATE SYSTEM ON V NEAR W ILL 7.4 A SPLITTING OF NEAR W
ILL 7.5 A COHOMOLOGICAL OBSTRUCTION TO THE EQUALITY T H V W =T H W .
. . . 113 7.6 AN EXTENSION OF T H W TOV 114 ASTERISQUE CONTENTS 7.7 THE
CONJUGATE SUPERCONNECTION A U: T 116 7.8 A LICHNEROWICZ FORMULA FOR A T
AND A T 118 8 A TAYLOR EXPANSION OF THE SUPERCONNECTION A ^ NEAR W 121
8.1 A TRIVIALIZATION OF A(T* (0 1) ^) § ALONG GEODESIES NORMAL TO Y
... 121 8.2 A TAYLOR EXPANSION FOR AI T X NEAR W , 122 8.3 THE
PROJECTION OF THE SUPERCONNECTION 93 128 9 THE ASYMPTOTICS OF
SUPERTRACES INVOLVING THE OPERATOR EXP(-B^ T ) FOR LARGE VALUES OF U, T
131 9.1 THE SPECTRUM OF B 2UT 133 9.2 A SCALING FORMULA . 134 9.3 TWO
INTERMEDIATE RESULTS 135 9.4 A FORMULA FOR P R F ^ H , W VP R W AND
ITS NORMAL DERIVATIVE ... 137 9.5 AN EMBEDDING OF F IN E 138 - 9.6 A
SOBOLEV NORM ON E 1 . . . I 140 9.7 ESTIMATES ON THE RESOLVENT OF A 144
9.8 REGULARIZING PROPERTIES OF THE RESOLVENT OF A 146 9.9 UNIFORM
ESTIMATES ON THE KERNEL F U (A ) 150 9.10 THE MATRIX STRUCTURE OF A AS
T * +00 153 9.11 THE ASYMPTOTICS OF THE OPERATOR F U {A^) AS T * +00
155 9.12 PROOF OF THEOREM 9.5 155 9.13 THE OPERATORS ^ A ,B,C,T * * * *
* 157 9.14 PROOF OF THEOREM 9.6 160 9.15 PROOF OF THEOREM 6.15 162 9.16
PROOF OF THEOREM 6.16 163 10 THE ASYMPTOTICS OF THE METRIC G {Y R)W) AS
T - +00 165 10.1 THE LIFT OF SECTIONS OF KER D Y TO SECTIONS OF KER A^
] ,-*** 165 10.2 THE LIFT OF SECTIONS OF KER D Y TO HARMONIC FORMS IN E
FO R 171 10.3 PROOF OF THEOREM 6.10 174 11 THE ANALYSIS OF THE TWO
PARAMETER SEMI-GROUP EXP(* A T ) IN THE RANGE UE]0,L],TG[0,I] 177
11.1 THE LIMIT AS U- OOF $TR S [AT HV EXP(-A2 )T )] 178 11.2
LOCALIZATION OF THE PROBLEM 179 11.3 A RESCALING OF THE NORMAL
COORDINATE Z O 182 11.4 A LOCAL COORDINATE SYSTEM NEAR W AND A
TRIVIALIZATION OF NYA(T^_S) S 182 SOCIETE MATHEMATIQUE DE FRANCE VI
CONTENTS 11.5 THE TAYLOR EXPANSION OF THE OPERATOR B U I 185 11.6
REPLACING X BY {T R X) VO . * 186 11.7 RESCALING OF THE .VARIABLE Z AND
OF THE CLIFFORD VARIABLES 187 11.8 THE MATRIX STRUCTURE OF I%%? /T 190
11.9 A FAMILY OF SOBOLEV SPACES WITH WEIGHTS 192 11.10 PROOF OF THEOREM
11.5 193 11.11 PROOF OF THEOREM 6.17 193 12 THE ANALYSIS OF THE KERNEL
OF F U (A 2U T/ J FOR T 0 AS U - 0 195 12.1 LOCALIZATION OF THE
PROBLEM 196 12.2 A LOCAL COORDINATE SYSTEM NEAR YO * W AND A
TRIVIALIZATION OF A(T^ ^X) 196 12.3 REPLACING THE FIBRE X BY (T R
X) YO 196 12.4 RESCALING OF THE VARIABLE Z AND OF THE HORIZONTAL
CLIFFORD VARIABLES . 197 12.5 THE ASYMPTOTICS OF THE OPERATOR L UV ^,, U
AS U * 0 198 12.6 PROOF OF THEOREM 6.8 . . 203 12.7 PROOF OF THE
FIRST HALF OF THEOREM 6.18 203 13 THE ANALYSIS OF THE TWO PARAMETER
OPERATOR EXP(* A T ) IN THE RANGE U E]0,1], T /U 213 13.1 A PROOF OF
THEOREM 6.9: THE PROBLEM IS LOCALIZABLE ON W 214 13.2 AN ORTHOGONAL
SPLITTING OF TX AND A CONNECTION ON TX 216 13.3 A LOCAL COORDINATE
SYSTEM NEAR YO * W AND A TRIVIALIZATION 217 13.4 REPLACING X BY (T R X)
YO ; 219 13.5 RESCALING OF Z AND OF THE HORIZONTAL CLIFFORD VARIABLES
220 13.6 A FORMULA FOR %%$! 222 13.7 THE ALGEBRAIC STRUCTURE OF THE
OPERATOR IE 3 ^ AS U * 0 225 13.8 THE MATRIX STRUCTURE OF THE OPERATOR
2*^? AS T * +OO 229 13.9 THE ASYMPTOTICS OF FR^^A^TK^^F^ 1 . 232
13.10 A FAMILY OF SOBOLEV SPACES WITH WEIGHTS 235 13.11 THE OPERATOR E
YO . 236 13.12 PROOF OF THEOREM 13.2 237 13.13 A PROOF OF THEOREM 6.19
237 AN EVALUATION OF THE LIMIT OI 6 UT T AS T * +OO 237 THE
CONNECTION 3V-VA(^S)§A(R-)A(T-(. 1 )X) 246 THE ALGEBRAIC STRUCTURE OF
%%VJ! AS U * 0 247 AN ESTIMATE ON 6 UIT / U - #* | 250 13.14 A PROOF
OF THE SECOND HALF OF THEOREM 6.18 251 ASTERISQUE CONTENTS - VII 14 A
PROOF OF THEOREM 0.2 259 14.1 A CLOSED FORM ON R+ X R+ 259 14.2 THE
ASYMPTOTICS OF THE 7 S 260 THE TERM 7{ 260 THE TERM / : 262 THE
TERM 7 264 THE TERM 7F 264 THE RIGHT-HAND SIDE OF (14.6) 265 14.3
MATCHING THE DIVERGENCES 266 14.4 PROOF OF THEOREM 0.2 266 15 A NEW
DERIVATION OF THE ASYMPTOTICS OF THE GENERALIZED SUPERTRACES ASSOCIATED
TO A SHORT EXACT SEQUENCE 267 15.1 A FAMILY OF IMMERSIONS 268 15.2 THE
SUPERCONNECTION 26 T 269 BIBLIOGRAPHY 273 SOCIETE MATHEMATIQUE DE FRANCE
|
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| bvnumber | BV011994249 |
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| discipline | Mathematik |
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| id | DE-604.BV011994249 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:19:52Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008117227 |
| oclc_num | 245713784 |
| open_access_boolean | |
| owner | DE-20 DE-355 DE-BY-UBR DE-29T DE-824 DE-384 DE-12 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-11 |
| owner_facet | DE-20 DE-355 DE-BY-UBR DE-29T DE-824 DE-384 DE-12 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-11 |
| physical | VII, 275 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Soc. Math. de France |
| record_format | marc |
| series | Astérisque |
| series2 | Astérisque |
| spelling | Bismut, Jean-Michel 1948- Verfasser (DE-588)141840056 aut Holomorphic families of immersions and higher analytic torsion forms Jean-Michel Bismut [Paris] Soc. Math. de France 1997 VII, 275 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Astérisque 244 Immersion Differentialgeometrie (DE-588)4191446-6 gnd rswk-swf Torsion (DE-588)4125469-7 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd rswk-swf Holomorphie (DE-588)4160484-2 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 s Immersion Differentialgeometrie (DE-588)4191446-6 s Torsion (DE-588)4125469-7 s DE-604 Holomorphie (DE-588)4160484-2 s Astérisque 244 (DE-604)BV002579439 244 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008117227&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bismut, Jean-Michel 1948- Holomorphic families of immersions and higher analytic torsion forms Astérisque Immersion Differentialgeometrie (DE-588)4191446-6 gnd Torsion (DE-588)4125469-7 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Holomorphie (DE-588)4160484-2 gnd |
| subject_GND | (DE-588)4191446-6 (DE-588)4125469-7 (DE-588)4031996-9 (DE-588)4160484-2 |
| title | Holomorphic families of immersions and higher analytic torsion forms |
| title_auth | Holomorphic families of immersions and higher analytic torsion forms |
| title_exact_search | Holomorphic families of immersions and higher analytic torsion forms |
| title_full | Holomorphic families of immersions and higher analytic torsion forms Jean-Michel Bismut |
| title_fullStr | Holomorphic families of immersions and higher analytic torsion forms Jean-Michel Bismut |
| title_full_unstemmed | Holomorphic families of immersions and higher analytic torsion forms Jean-Michel Bismut |
| title_short | Holomorphic families of immersions and higher analytic torsion forms |
| title_sort | holomorphic families of immersions and higher analytic torsion forms |
| topic | Immersion Differentialgeometrie (DE-588)4191446-6 gnd Torsion (DE-588)4125469-7 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Holomorphie (DE-588)4160484-2 gnd |
| topic_facet | Immersion Differentialgeometrie Torsion Komplexe Mannigfaltigkeit Holomorphie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008117227&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002579439 |
| work_keys_str_mv | AT bismutjeanmichel holomorphicfamiliesofimmersionsandhigheranalytictorsionforms |