Introduction to foliations and Lie groupoids:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, U.K.
Cambridge University Press
2008
|
| Ausgabe: | transferred to digital print. |
| Schriftenreihe: | Cambridge studies in advanced mathematics
91 |
| Schlagworte: | |
| Online-Zugang: | Sample text Publisher description Table of contents Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 166-169) and index |
| Beschreibung: | IX, 173 S. Ill., graph. Darst. 24 cm |
| ISBN: | 0521831970 9780521831970 |
Internformat
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| 245 | 1 | 0 | |a Introduction to foliations and Lie groupoids |c I. Moerdijk and J. Mrc̆un |
| 250 | |a transferred to digital print. | ||
| 264 | 1 | |a Cambridge, U.K. |b Cambridge University Press |c 2008 | |
| 300 | |a IX, 173 S. |b Ill., graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Cambridge studies in advanced mathematics |v 91 | |
| 500 | |a Includes bibliographical references (p. 166-169) and index | ||
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Datensatz im Suchindex
| _version_ | 1804137600698548224 |
|---|---|
| adam_text | Contents
Preface
page vii
Prerequisites I
Foliations
4
1.1
Definition and first examples
5
1.2
Alternative definitions of foliations
9
1.3
Constructions of foliations
14
Holonomy and stability
19
2.1
Holonomy
20
2.2
Riemannian foliations
25
2.3
Local
Reeb
stability
30
2.4
Orbifolds
34
2.5
Global
Reeb
stability in codimension
1 44
2.6
Thurston s stability theorem
49
Two classical theorems
56
3.1
Haefliger s theorem
57
3.1.1
Review of Morse functions
58
3.1.2
Morse functions into codimension
1
foliations
60
3.1.3
Proof of Haefliger s theorem
62
3.2
Novikov s theorem
65
3.2.1
Vanishing cycles
66
3.2.2
Existence of a compact leaf
71
3.2.3
Existence of a Reeb component
77
Molino s theory
8
1
4.1
Transverse parallelizability
82
4.1.1
Homogeneous foliations
82
4.1.2
Transversely parallelizable foliations
86
vi
Contents
4.2
Principal
bundles
92
4.2.1
Connections on principal bundles
93
4.2.2
Transverse principal bundles
98
4.3
Lie foliations and Molino s theorem
101
4.3.1
Lie foliations
102
4.3.2
The Darboux cover
103
4.3.3
Molino s structure theorem
108
5
Lie groupoids
110
5.1
Definition and first examples
111
5.2
The monodromy and holonomy groupoids
117
5.3
Some general constructions
121
5.4
Equivalence of Lie groupoids
127
5.5
Etale
groupoids
134
5.6
Proper groupoids and orbifolds
140
5.7
Principal bundles over Lie groupoids
144
6
Lie algebroids
149
6.1
The Lie algebroid of a Lie groupoid
150
6.2
Definition and examples of Lie algebroids
153
6.3
Lie theory for Lie groupoids
157
6.4
Integrabili
ty and developable foliations
160
References and further reading
166
Index
170
|
| adam_txt |
Contents
Preface
page vii
Prerequisites I
Foliations
4
1.1
Definition and first examples
5
1.2
Alternative definitions of foliations
9
1.3
Constructions of foliations
14
Holonomy and stability
19
2.1
Holonomy
20
2.2
Riemannian foliations
25
2.3
Local
Reeb
stability
30
2.4
Orbifolds
34
2.5
Global
Reeb
stability in codimension
1 44
2.6
Thurston's stability theorem
49
Two classical theorems
56
3.1
Haefliger's theorem
57
3.1.1
Review of Morse functions
58
3.1.2
Morse functions into codimension
1
foliations
60
3.1.3
Proof of Haefliger's theorem
62
3.2
Novikov's theorem
65
3.2.1
Vanishing cycles
66
3.2.2
Existence of a compact leaf
71
3.2.3
Existence of a Reeb component
77
Molino's theory
8
1
4.1
Transverse parallelizability
82
4.1.1
Homogeneous foliations
82
4.1.2
Transversely parallelizable foliations
86
vi
Contents
4.2
Principal
bundles
92
4.2.1
Connections on principal bundles
93
4.2.2
Transverse principal bundles
98
4.3
Lie foliations and Molino's theorem
101
4.3.1
Lie foliations
102
4.3.2
The Darboux cover
103
4.3.3
Molino's structure theorem
108
5
Lie groupoids
110
5.1
Definition and first examples
111
5.2
The monodromy and holonomy groupoids
117
5.3
Some general constructions
121
5.4
Equivalence of Lie groupoids
127
5.5
Etale
groupoids
134
5.6
Proper groupoids and orbifolds
140
5.7
Principal bundles over Lie groupoids
144
6
Lie algebroids
149
6.1
The Lie algebroid of a Lie groupoid
150
6.2
Definition and examples of Lie algebroids
153
6.3
Lie theory for Lie groupoids
157
6.4
Integrabili
ty and developable foliations
160
References and further reading
166
Index
170 |
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| isbn | 0521831970 9780521831970 |
| language | English |
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| spelling | Moerdijk, Izak Verfasser aut Introduction to foliations and Lie groupoids I. Moerdijk and J. Mrc̆un transferred to digital print. Cambridge, U.K. Cambridge University Press 2008 IX, 173 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 91 Includes bibliographical references (p. 166-169) and index aFoliations (Mathematics) aLie groupoids Lie-Gruppoid (DE-588)4224180-7 gnd rswk-swf Lie-Algebroid (DE-588)4630863-5 gnd rswk-swf Riemannsche Blätterung (DE-588)4195597-3 gnd rswk-swf Riemannsche Blätterung (DE-588)4195597-3 s Lie-Gruppoid (DE-588)4224180-7 s Lie-Algebroid (DE-588)4630863-5 s DE-604 Mrc̆un, J. Sonstige oth Cambridge studies in advanced mathematics 91 (DE-604)BV000003678 91 http://www.loc.gov/catdir/samples/cam041/2003046172.html Sample text http://www.loc.gov/catdir/description/cam032/2003046172.html Publisher description http://www.loc.gov/catdir/toc/cam031/2003046172.html Table of contents Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016466452&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moerdijk, Izak Introduction to foliations and Lie groupoids Cambridge studies in advanced mathematics aFoliations (Mathematics) aLie groupoids Lie-Gruppoid (DE-588)4224180-7 gnd Lie-Algebroid (DE-588)4630863-5 gnd Riemannsche Blätterung (DE-588)4195597-3 gnd |
| subject_GND | (DE-588)4224180-7 (DE-588)4630863-5 (DE-588)4195597-3 |
| title | Introduction to foliations and Lie groupoids |
| title_auth | Introduction to foliations and Lie groupoids |
| title_exact_search | Introduction to foliations and Lie groupoids |
| title_exact_search_txtP | Introduction to foliations and Lie groupoids |
| title_full | Introduction to foliations and Lie groupoids I. Moerdijk and J. Mrc̆un |
| title_fullStr | Introduction to foliations and Lie groupoids I. Moerdijk and J. Mrc̆un |
| title_full_unstemmed | Introduction to foliations and Lie groupoids I. Moerdijk and J. Mrc̆un |
| title_short | Introduction to foliations and Lie groupoids |
| title_sort | introduction to foliations and lie groupoids |
| topic | aFoliations (Mathematics) aLie groupoids Lie-Gruppoid (DE-588)4224180-7 gnd Lie-Algebroid (DE-588)4630863-5 gnd Riemannsche Blätterung (DE-588)4195597-3 gnd |
| topic_facet | aFoliations (Mathematics) aLie groupoids Lie-Gruppoid Lie-Algebroid Riemannsche Blätterung |
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