Intersection cohomology: [notes of a seminar on intersection homology, which met weekly during the spring 1983 at the University of Bern, Switzerland]
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
1984
|
| Series: | Progress in mathematics
50 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 238 S. |
| ISBN: | 0817632743 3764332743 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | viii
TABLE OF CONTENTS
I. INTRODUCTION TO PIECEWISE LINEAR INTERSECTION HOMOLOGY
by A. Haefliger
SI. Pseudomanifolds and stratifications 1
$2 Geometric chains on PL space 5
S3 Definition of intersection homology 10
§4 List of the main properties of intersection homology 12
S5 Examples: pseudomanifolds with isolated singularities 14
References 21
II. FROM PL TO SHEAF THEORY
by N. Habegger
50 Introduction 23
§1 The calculus of chains 24
§2 Intersection homology of a product with Euclidean space 25
53 Intersection homology of a cone 28
54 The local intersection homology groups .... 29
§5 The sheaves IC 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. Borel
(with the collaboration of N. Spaltenstein)
51 Sheaf theory 47
A. Generalities 47
B. Cohomological dimension and bounded resolutions 53
ix
§2 Deligne s sheaf. First axiomatic characterisation 60
§3 Constructibility 68
§4 Reformulation of the axioms and topological invariance of IC. 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 c soft 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
i
C. The functors f, and f* . Verdier duality 127
§8 Biduality on a pseudomanifold 133
A. Constructibility 133
B. Biduality 137
§9 Pairings and Poincare duality in IC 143
A. Some morphisms 143
B. Poincare 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 ft et f* 184
§2 Le foncteur f, 186
§3 Le foncteur f 197
Append ice 204
References 207
VII. WITT SPACE COBORDISM THEORY (after P. Siegel)
by H. Goresky 2O9
References 214
X
VIII. LEFSCHETZ FIXED POINT THEOREM AND INTERSECTION HOMOLOGY
by M. Goresky and R. MacPherson 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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| classification_tum | MAT 552f |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000282328 |
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| indexdate | 2024-07-09T15:11:37Z |
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| isbn | 0817632743 3764332743 |
| language | English |
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| physical | X, 238 S. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
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| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Intersection cohomology [notes of a seminar on intersection homology, which met weekly during the spring 1983 at the University of Bern, Switzerland] A. Borel et al. Boston [u.a.] Birkhäuser 1984 X, 238 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 50 Homologietheorie (DE-588)4141714-8 gnd rswk-swf Schnittraum (DE-588)4300596-2 gnd rswk-swf Homologie (DE-588)4141951-0 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 Progress in mathematics 50 (DE-604)BV000004120 50 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000171546&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Intersection cohomology [notes of a seminar on intersection homology, which met weekly during the spring 1983 at the University of Bern, Switzerland] Progress in mathematics Homologietheorie (DE-588)4141714-8 gnd Schnittraum (DE-588)4300596-2 gnd Homologie (DE-588)4141951-0 gnd Garbentheorie (DE-588)4155956-3 gnd Schnitttheorie (DE-588)4179890-9 gnd |
| subject_GND | (DE-588)4141714-8 (DE-588)4300596-2 (DE-588)4141951-0 (DE-588)4155956-3 (DE-588)4179890-9 (DE-588)4143413-4 (DE-588)1071861417 |
| title | Intersection cohomology [notes of a seminar on intersection homology, which met weekly during the spring 1983 at the University of Bern, Switzerland] |
| title_auth | Intersection cohomology [notes of a seminar on intersection homology, which met weekly during the spring 1983 at the University of Bern, Switzerland] |
| title_exact_search | Intersection cohomology [notes of a seminar on intersection homology, which met weekly during the spring 1983 at the University of Bern, Switzerland] |
| title_full | Intersection cohomology [notes of a seminar on intersection homology, which met weekly during the spring 1983 at the University of Bern, Switzerland] A. Borel et al. |
| title_fullStr | Intersection cohomology [notes of a seminar on intersection homology, which met weekly during the spring 1983 at the University of Bern, Switzerland] A. Borel et al. |
| title_full_unstemmed | Intersection cohomology [notes of a seminar on intersection homology, which met weekly during the spring 1983 at the University of Bern, Switzerland] A. Borel et al. |
| title_short | Intersection cohomology |
| title_sort | intersection cohomology notes of a seminar on intersection homology which met weekly during the spring 1983 at the university of bern switzerland |
| title_sub | [notes of a seminar on intersection homology, which met weekly during the spring 1983 at the University of Bern, Switzerland] |
| topic | Homologietheorie (DE-588)4141714-8 gnd Schnittraum (DE-588)4300596-2 gnd Homologie (DE-588)4141951-0 gnd Garbentheorie (DE-588)4155956-3 gnd Schnitttheorie (DE-588)4179890-9 gnd |
| topic_facet | Homologietheorie Schnittraum Homologie Garbentheorie Schnitttheorie Aufsatzsammlung Konferenzschrift 1983 Bern |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000171546&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT borelarmand intersectioncohomologynotesofaseminaronintersectionhomologywhichmetweeklyduringthespring1983attheuniversityofbernswitzerland |