Topology of singular spaces and constructible sheaves:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Basel
Birkhäuser
2003
|
| Series: | Monografie matematyczne
63 : New series |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 452 S. |
| ISBN: | 376432189X |
Staff View
MARC
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| 100 | 1 | |a Schürmann, Jörg |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Topology of singular spaces and constructible sheaves |c Jörg Schürmann |
| 264 | 1 | |a Basel |b Birkhäuser |c 2003 | |
| 300 | |a X, 452 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Monografie matematyczne |v 63 : New series | |
| 502 | |a Zugl.: Hamburg, Univ., Habil.-Schr., 2000 | ||
| 650 | 4 | |a Algebraic spaces | |
| 650 | 4 | |a Functions of complex variables | |
| 650 | 4 | |a Homology theory | |
| 650 | 4 | |a Sheaf theory | |
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Record in the Search Index
| _version_ | 1808135308344033280 |
|---|---|
| adam_text |
CONTENTS
INTRODUCTION
1
1
THOM-SEBASTIANI
THEOREM
FOR
CONSTRUCTIBLE
SHEAVES
17
INTRODUCTION
.
17
1.1
MILNOR
FIBRATION
.
23
1.1.1
COHOMOLOGICAL
VERSION
OF
A
MILNOR
FIBRATION
.
24
1.1.2
EXAMPLES
.
32
1.2
THOM-SEBASTIANI
THEOREM
.
38
1.2.1
PRELIMINARIES
AND
THOM-SEBASTIANI
FOR
ADDITIVE
FUNCTIONS
.
38
1.2.2
THOM-SEBASTIANI
THEOREM
FOR
SHEAVES
.
50
1.3
THE
THOM-SEBASTIANI
ISOMORPHISM
IN
THE
DERIVED
CATEGORY
.
62
1.4
APPENDIX:
KIINNETH
FORMULA
.
74
2
CONSTRUCTIBLE
SHEAVES
IN
GEOMETRIC
CATEGORIES
81
INTRODUCTION
.
81
2.0.1
THE
BASIC
RESULTS
.
81
2.0.2
DEFINABLE
SPACES
.
89
2.1
GEOMETRIC
CATEGORIES
.
93
2.2
CONSTRUCTIBLE
SHEAVES
.
98
2.3
CONSTRUCTIBLE
FUNCTIONS
.
122
3
LOCALIZATION
RESULTS
FOR
EQUIVARIANT
CONSTRUCTIBLE
SHEAVES
141
INTRODUCTION
.
141
3.1
EQUIVARIANT
SHEAVES
.
149
3.1.1
EQUIVARIANT
SHEAVES
AND
MONODROMIC
COMPLEXES
.
149
3.1.2
EQUIVARIANT
DERIVED
CATEGORIES
.
155
3.1.3
EXAMPLES
AND
STALK
FORMULAE
.
159
3.2
LOCALIZATION
RESULTS
FOR
ADDITIVE
FUNCTIONS
.
170
3.3
LOCALIZATION
RESULTS
FOR
GROTHENDIECK
GROUPS
AND
TRACE
FORMULAE
.
.
176
3.3.1
GROTHENDIECK
GROUPS
.
176
3.3.2
TRACE
FORMULAE
.
192
3.4
EQUIVARIANT
COHOMOLOGY
.
200
X
CONTENTS
4
STRATIFICATION
THEORY
AND
CONSTRUCTIBLE
SHEAVES
207
INTRODUCTION
.
207
4.1
STRATIFICATION
THEORY
.
217
4.1.1
A
COHOMOLOGICAL
VERSION
OF
THE
FIRST
ISOTOPY
LEMMA
.
217
4.1.2
COMPARISON
OF
DIFFERENT
REGULARITY
CONDITIONS
.
223
4.1.3
MICRO-LOCAL
CHARACTERIZATION
OF
CONSTRUCTIBLE
SHEAVES
.
229
4.2
CONSTRUCTIBLE
SHEAVES
ON
STRATIFIED
SPACES
.
232
4.2.1
COHOMOLOGICALLY
CONE-LIKE
STRATIFICATIONS
.
232
4.2.2
STABILITY
RESULTS
FOR
CONSTRUCTIBLE
SHEAVES
.
241
4.3
BASE
CHANGE
PROPERTIES
.
252
4.3.1
SOME
CONSTRUCTIONS
FOR
STRATIFICATIONS
.
253
4.3.2
BASE
CHANGE
ISOMORPHISMS
.
259
5
MORSE
THEORY
FOR
CONSTRUCTIBLE
SHEAVES
269
INTRODUCTION
.
269
5.0.1
REAL
STRATIFIED
MORSE
THEORY
.
270
5.0.2
COMPLEX
STRATIFIED
MORSE
THEORY
.
281
5.0.3
INTRODUCTION
TO
CHARACTERISTIC
CYCLES
.
283
5.1
STRATIFIED
MORSE
THEORY,
PART
I
.
296
5.1.1
LOCAL
MORSE
DATA
.
296
5.1.2
NORMAL
MORSE
DATA
.
307
5.1.3
MORSE
THEORY
FOR
A
STRATIFIED
SPACE
WITH
CORNERS
.
316
5.2
CHARACTERISTIC
CYCLES
AND
INDEX
FORMULAE
.
320
5.2.1
INDEX
FORMULAE
AND
EULER
OBSTRUCTION
.
321
5.2.2
A
SPECIALIZATION
ARGUMENT
.
328
5.3
STRATIFIED
MORSE
THEORY,
PART
II
.
334
5.3.1
NORMAL
MORSE
DATA
ARE
INDEPENDENT
OF
CHOICES
.
334
5.3.2
SPLITTING
OF
THE
LOCAL
MORSE
DATA
.
345
5.3.3
NORMAL
MORSE
DATA
AND
MICRO-LOCALIZATION
.
355
5.4
VANISHING
CYCLES
.
361
6
VANISHING
THEOREMS
FOR
CONSTRUCTIBLE
SHEAVES
375
INTRODUCTION:
RESULTS
AND
EXAMPLES
.
375
6.0.1
(CO)STALK
PROPERTIES
.
375
6.0.2
INTERSECTION
(CO)HOMOLOGY
AND
PERVERSE
SHEAVES
.
381
6.0.3
VANISHING
RESULTS
IN
THE
COMPLEX
CONTEXT
.
385
6.0.4
NEARBY
AND
VANISHING
CYCLES
.
402
6.0.5
ARTIN-GROTHENDIECK
TYPE
THEOREMS
.
408
6.0.6
APPLICATIONS
TO
CONSTRUCTIBLE
FUNCTIONS
.
412
6.1
PROOF
OF
THE
RESULTS
.
414
BIBLIOGRAPHY
433
INDEX
447 |
| any_adam_object | 1 |
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| author_facet | Schürmann, Jörg |
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| dewey-full | 514/.224 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.224 |
| dewey-search | 514/.224 |
| dewey-sort | 3514 3224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| isbn | 376432189X |
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| spelling | Schürmann, Jörg Verfasser aut Topology of singular spaces and constructible sheaves Jörg Schürmann Basel Birkhäuser 2003 X, 452 S. txt rdacontent n rdamedia nc rdacarrier Monografie matematyczne 63 : New series Zugl.: Hamburg, Univ., Habil.-Schr., 2000 Algebraic spaces Functions of complex variables Homology theory Sheaf theory Singulärer Raum (DE-588)4181528-2 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Garbentheorie (DE-588)4155956-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Algebraische Topologie (DE-588)4120861-4 s Garbentheorie (DE-588)4155956-3 s Singulärer Raum (DE-588)4181528-2 s DE-604 Monografie matematyczne 63 : New series (DE-604)BV000003532 63 : New series DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010441719&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schürmann, Jörg Topology of singular spaces and constructible sheaves Monografie matematyczne Algebraic spaces Functions of complex variables Homology theory Sheaf theory Singulärer Raum (DE-588)4181528-2 gnd Algebraische Topologie (DE-588)4120861-4 gnd Garbentheorie (DE-588)4155956-3 gnd |
| subject_GND | (DE-588)4181528-2 (DE-588)4120861-4 (DE-588)4155956-3 (DE-588)4113937-9 |
| title | Topology of singular spaces and constructible sheaves |
| title_auth | Topology of singular spaces and constructible sheaves |
| title_exact_search | Topology of singular spaces and constructible sheaves |
| title_full | Topology of singular spaces and constructible sheaves Jörg Schürmann |
| title_fullStr | Topology of singular spaces and constructible sheaves Jörg Schürmann |
| title_full_unstemmed | Topology of singular spaces and constructible sheaves Jörg Schürmann |
| title_short | Topology of singular spaces and constructible sheaves |
| title_sort | topology of singular spaces and constructible sheaves |
| topic | Algebraic spaces Functions of complex variables Homology theory Sheaf theory Singulärer Raum (DE-588)4181528-2 gnd Algebraische Topologie (DE-588)4120861-4 gnd Garbentheorie (DE-588)4155956-3 gnd |
| topic_facet | Algebraic spaces Functions of complex variables Homology theory Sheaf theory Singulärer Raum Algebraische Topologie Garbentheorie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010441719&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003532 |
| work_keys_str_mv | AT schurmannjorg topologyofsingularspacesandconstructiblesheaves |