Intersection cohomology:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2008
|
| Ausgabe: | reprint. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 234 S. |
| ISBN: | 9780817647643 |
Internformat
MARC
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016539907 | ||
Datensatz im Suchindex
| _version_ | 1804137716810514432 |
|---|---|
| adam_text | viii
TABLE OF
CONTENTS
I. INTRODUCTION TO PIECEWISE
LINEAR
INTERSECTION
HOMOLOGY
by A. Haefliger
§1.
Pseudomanifolds and stratifications
......................... 1
§2
Geometr
ic
chains on PL space
................................ 5
§3
Definition of intersection homology
......................... 10
§4
List of the main properties of intersection homology
........ 12
§5
Examples:
pseuđomanifolđs
with isolated singularities
....... 1*
References
...................................................... 21
II. FROM PL TO SHEAF THEORY
by
N.
Habegger
§0
Introduction
................................................ 23
SI The calculus of chains
...................................... 24
§2
Intersection homology of a product with Euclidean space
..... 25
§3
Intersection homology of a cone
............................. 28
§4
The local intersection homology groups
...................-... 29
§5
The sheaves
1С
are soft
..................................... 32
§6
Axioms for the intersection homology sheaves
................ 33
III. A SAMPLE COMPUTATION OF INTERSECTION HOMOLOGY
by M. Goresky and R. MacPherson
35
IV. PSEUDOMANIFOLD STRUCTURES ON COMPLEX ANALYTIC SPACES
by
N.
A Campo 41
References
.................................................... 45
V. SHEAF THEORETIC INTERSECTION COHOMOLOGY
by
A. Borei
(with the collaboration of
N. Spaltenstein)
§1
Sheaf theory
................................................ 47
A. Generalities
........................................... 47
B. Cohomological dimension and bounded resolutions
........ 53
ix
§2
Deligne s
sheaf. First axiomatic characterisation
...........
6O
§3
Constructibility
............................................ 68
§4
Reformulation of the axioms and topological
invariance
of
1С. 86
§5
The derived category of sheaves
............................. 97
A. Triangles and long exact sequences
..................... 97
B. Further properties of distinguished triangles
.......... 102
C. The derived category of Sh(X)
.......................... 108
§6
Flat and
с
-sof
t
sheaves
..................................... 113
§7
The dual of a complex of sheaves. Verdier duality
........... 119
A. The dualizing sheaf and homology
....................... 119
B. The dual of a complex of sheaves
....................... 121
C. The functors f, and f
.
Verdier duality
............... 127
§8
Biduality on a pseudomanifold
.............................. 133
A. Constructibility
...................................... 133
B. Biduality
.............................................. 137
§9
Pairings and
Poincaré
duality in
1С ........................ 143.
A. Some morphisms
........................................ 143
B. Poincaré
duality
...................................... 146
C. Pairings
.............................................. 151
§10
Some formulae in derived categories of sheaves
............. 155
A. Continuous maps
....................................... 155
B. Stratified maps
....................................... 163
C
.
Some identities on products
........................... 170
References
..................................................... 182
VI.
LES
FONCTEURS
DE LA CATEGORIE DES FAISCEAUX
ASSOCIES A UNE APPLICATION CONTINUE
by P.P.
Grivel
183
§1
Les foncteurs f t et f
* .....................................184
§2
Le foncteur f,
............................................ 186
§3
Le foncteur f
........................................... 197
Appendice
.................................................. 204
Références
....................................................207
VII.
WITT SPACE COBORDISM THEORY (after P.
Siegel)
by M. Goresky 2O9
References
.....................................................214
χ
VIII.
LEFSCHETZ FIXED POINT THEOREM AND INTERSECTION HOMOLOGY
by M. Goresky and R. MacPhetson
215
References
.................................................... 219
IX. PROBLEMS AND BIBLIOGRAPHY ON INTERSECTION HOMOLOGY
by M. Goresky and R. MacPherson
221
References
.................................................... 229
AUTHORS ADDRESSES
.............................................. 235
|
| adam_txt |
viii
TABLE OF
CONTENTS
I. INTRODUCTION TO PIECEWISE
LINEAR
INTERSECTION
HOMOLOGY
by A. Haefliger
§1.
Pseudomanifolds and stratifications
. 1
§2
Geometr
ic
chains on PL space
. 5
§3
Definition of intersection homology
. 10
§4
List of the main properties of intersection homology
. 12
§5
Examples:
pseuđomanifolđs
with isolated singularities
. 1*
References
. 21
II. FROM PL TO SHEAF THEORY
by
N.
Habegger
§0
Introduction
. 23
SI The calculus of chains
. 24
§2
Intersection homology of a product with Euclidean space
. 25
§3
Intersection homology of a cone
. 28
§4
The local intersection homology groups
.-. 29
§5
The sheaves
1С
are soft
. 32
§6
Axioms for the intersection homology sheaves
. 33
III. A SAMPLE COMPUTATION OF INTERSECTION HOMOLOGY
by M. Goresky and R. MacPherson
35
IV. PSEUDOMANIFOLD STRUCTURES ON COMPLEX ANALYTIC SPACES
by
N.
A'Campo 41
References
. 45
V. SHEAF THEORETIC INTERSECTION COHOMOLOGY
by
A. Borei
(with the collaboration of
N. Spaltenstein)
§1
Sheaf theory
. 47
A. Generalities
. 47
B. Cohomological dimension and bounded resolutions
. 53
ix
§2
Deligne's
sheaf. First axiomatic characterisation
.
6O
§3
Constructibility
. 68
§4
Reformulation of the axioms and topological
invariance
of
1С. 86
§5
The derived category of sheaves
. 97
A. Triangles and long exact sequences
. 97
B. Further properties of distinguished triangles
. 102
C. The derived category of Sh(X)
. 108
§6
Flat and
с
-sof
t
sheaves
. 113
§7
The dual of a complex of sheaves. Verdier duality
. 119
A. The dualizing sheaf and homology
. 119
B. The dual of a complex of sheaves
. 121
C. The functors f, and f"
.
Verdier duality
. 127
§8
Biduality on a pseudomanifold
. 133
A. Constructibility
. 133
B. Biduality
. 137
§9
Pairings and
Poincaré
duality in
1С . 143.
A. Some morphisms
. 143
B. Poincaré
duality
. 146
C. Pairings
. 151
§10
Some formulae in derived categories of sheaves
. 155
A. Continuous maps
. 155
B. Stratified maps
. 163
C
.
Some identities on products
. 170
References
. 182
VI.
LES
FONCTEURS
DE LA CATEGORIE DES FAISCEAUX
ASSOCIES A UNE APPLICATION CONTINUE
by P.P.
Grivel
183
§1
Les foncteurs f t et f
* .184
§2
Le foncteur f,
. 186
§3
Le foncteur f"
. 197
Appendice
. 204
Références
.207
VII.
WITT SPACE COBORDISM THEORY (after P.
Siegel)
by M. Goresky 2O9
References
.214
χ
VIII.
LEFSCHETZ FIXED POINT THEOREM AND INTERSECTION HOMOLOGY
by M. Goresky and R. MacPhetson
215
References
. 219
IX. PROBLEMS AND BIBLIOGRAPHY ON INTERSECTION HOMOLOGY
by M. Goresky and R. MacPherson
221
References
. 229
AUTHORS ADDRESSES
. 235 |
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| genre_facet | Aufsatzsammlung Konferenzschrift 1983 Bern |
| id | DE-604.BV023356373 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:07:14Z |
| indexdate | 2024-07-09T21:16:43Z |
| institution | BVB |
| isbn | 9780817647643 |
| language | English |
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| spelling | Intersection cohomology A. Borel et al. reprint. Boston [u.a.] Birkhäuser 2008 X, 234 S. txt rdacontent n rdamedia nc rdacarrier Homologie (DE-588)4141951-0 gnd rswk-swf Homologietheorie (DE-588)4141714-8 gnd rswk-swf Schnittraum (DE-588)4300596-2 gnd rswk-swf Garbentheorie (DE-588)4155956-3 gnd rswk-swf Schnitttheorie (DE-588)4179890-9 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content (DE-588)1071861417 Konferenzschrift 1983 Bern gnd-content Schnitttheorie (DE-588)4179890-9 s Homologie (DE-588)4141951-0 s DE-604 Schnittraum (DE-588)4300596-2 s Homologietheorie (DE-588)4141714-8 s Garbentheorie (DE-588)4155956-3 s Borel, Armand 1923-2003 Sonstige (DE-588)119089106 oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016539907&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Intersection cohomology Homologie (DE-588)4141951-0 gnd Homologietheorie (DE-588)4141714-8 gnd Schnittraum (DE-588)4300596-2 gnd Garbentheorie (DE-588)4155956-3 gnd Schnitttheorie (DE-588)4179890-9 gnd |
| subject_GND | (DE-588)4141951-0 (DE-588)4141714-8 (DE-588)4300596-2 (DE-588)4155956-3 (DE-588)4179890-9 (DE-588)4143413-4 (DE-588)1071861417 |
| title | Intersection cohomology |
| title_auth | Intersection cohomology |
| title_exact_search | Intersection cohomology |
| title_exact_search_txtP | Intersection cohomology |
| title_full | Intersection cohomology A. Borel et al. |
| title_fullStr | Intersection cohomology A. Borel et al. |
| title_full_unstemmed | Intersection cohomology A. Borel et al. |
| title_short | Intersection cohomology |
| title_sort | intersection cohomology |
| topic | Homologie (DE-588)4141951-0 gnd Homologietheorie (DE-588)4141714-8 gnd Schnittraum (DE-588)4300596-2 gnd Garbentheorie (DE-588)4155956-3 gnd Schnitttheorie (DE-588)4179890-9 gnd |
| topic_facet | Homologie Homologietheorie Schnittraum Garbentheorie Schnitttheorie Aufsatzsammlung Konferenzschrift 1983 Bern |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016539907&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT borelarmand intersectioncohomology |