On the topology of isolated singularities in analytic spaces:
Gespeichert in:
| Format: | Elektronisch E-Book |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Basel ; Boston ; Berlin
Birkhäuser
2006
|
| Schriftenreihe: | Progress in mathematics
241 |
| Schlagworte: | |
| Online-Zugang: | BTU01 TUM01 UBA01 UBM01 UBR01 UBT01 UPA01 Volltext Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 221 - 233 |
| Beschreibung: | 1 Online-Ressource (XIV, 238 S.) Ill., graph. Darst. |
| ISBN: | 3764373229 9783764373955 |
| DOI: | 10.1007/3-7643-7395-4 |
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Datensatz im Suchindex
| _version_ | 1804136327340359680 |
|---|---|
| adam_text | Contents
Preface xiii
Introduction 1
Acknowledgments 9
I A Fast Trip Through the Classical Theory
1.1 An example: the Pham Brieskorn polynomials 11
1.2 The local conical structure 14
1.3 Ehresmann s fibration lemma 17
1.4 Milnor s fibration theorem for real singularities 18
1.5 Open book decompositions and fibred knots 21
1.6 On Milnor s fibration theorem for complex singularities .... 22
1.7 The join of Pham and the topology of the Milnor fibre.
The Milnor number 25
1.8 Exotic spheres and the topology of the link 30
II Motions in Plane Geometry and the 3 dimensional
Brieskorn Manifolds
II. 1 Groups of motions in the 2 sphere.
The polyhedral groups 36
11.2 Triangle groups and the classical plane geometries 42
11.3 The 3 sphere as a Lie group and its finite subgroups 47
11.4 Brieskorn manifolds and Klein s theorem 50
11.5 The group PSL(2,R) and its universal cover SL(2,R) 55
11.6 Milnor s theorem for the 3 dimensional Brieskorn
manifolds. The hyperbolic case 57
11.7 Brieskorn Hamm complete intersections.
The theorem of Neumann 60
11.8 Remarks 62
x Contents
III 3 dimensioual Lie Groups and Surface Singularities
111.1 Quasi Homogeneous surface singularities 65
111.2 3 manifolds whose universal covering is a Lie group 71
111.3 Lie groups and singularities I:
quasi homogeneous singularities 75
111.4 Lie groups and singularities II: the cusps 80
111.5 Lie groups and singularities III:
the Abelian and £+(2) cases 82
111.6 A uniform picture of 3 dimensional Lie groups 85
111.7 Lie algebras and the Gorenstein property 87
111.8 Remarks 88
IV Within the Realm of the General Index Theorem
IV. 1 A review of characteristic classes 92
IV.2 On Hirzebruch s theorems about the signature
and Riemann Roch 97
IV.3 Spin and Spinc structures on 4 manifolds.
Rochlin s theorem 102
IV.4 Spin and Spin0 structures on complex surfaces.
Rochlin s theorem 105
IV.5 A review of surface singularities 110
IV.6 Gorenstein and numerically Gorenstein singularities 116
IV.7 An application of Riemann Roch: Laufer s formula 121
IV.8 Geometric genus, spinc structures and
characteristic divisors 126
IV.9 On the signature of smoothings of surface singularities .... 128
IV. 10 On the Rochlin fi invariant for links
of surface singularities 131
IV. 11 Comments on new 3 manifolds invariants
and surface singularities 134
V On the Geometry and Topology of Quadrics in CPn
V.I The topology of a quadric in CPn 138
V.2 The space CPn as a double mapping cylinder 141
V.3 The orthogonal group SO(n+l,R) and
the geometry of CPn 143
V.4 Cohomogeneity 1 actions of SO(3) on CP2 and S4 148
V.5 The Arnold Kuiper Massey theorem 150
VI Real Singularities and Complex Geometry
VI.1 The space of Siegel leaves of a linear flow 157
VI.2 Real singularities and the Lopez de
Medrano Verjovsky Meersseman manifolds 163
VI.3 Real singularities and holomorphic vector fields 167
VI.4 On the topology of certain real hypersurface singularities . . . 170
Contents xi
VII Real Singularities with a Milnor Fibration
VII.1 Milnor s fibration theorem revisited 175
VII.2 The strong Milnor condition 177
VII.3 Real singularities of the Pham Brieskorn type 181
VII.4 Twisted Pham Brieskorn singularities and
the strong Milnor condition 187
VII.5 On the topology of the twisted
Pham Brieskorn singularities 191
VII.6 Stability of the Milnor conditions under perturbations 194
VII.7 Remarks and open problems 196
VIII Real Singularities and Open Book Decompositions of the 3 sphere
VIII. 1 On the resolution of embedded complex plane curves 200
VIII.2 The resolution and Seifert graphs 204
VIII.3 Seifert links and horizontal fibrations 206
VIII.4 An example 209
VIII.5 Resolution and topology of the singularities
z z2 + z zx =0 213
VIII.6 On singularities of the form fg 216
Bibliography 221
Index 235
|
| adam_txt |
Contents
Preface xiii
Introduction 1
Acknowledgments 9
I A Fast Trip Through the Classical Theory
1.1 An example: the Pham Brieskorn polynomials 11
1.2 The local conical structure 14
1.3 Ehresmann's fibration lemma 17
1.4 Milnor's fibration theorem for real singularities 18
1.5 Open book decompositions and fibred knots 21
1.6 On Milnor's fibration theorem for complex singularities . 22
1.7 The join of Pham and the topology of the Milnor fibre.
The Milnor number 25
1.8 Exotic spheres and the topology of the link 30
II Motions in Plane Geometry and the 3 dimensional
Brieskorn Manifolds
II. 1 Groups of motions in the 2 sphere.
The polyhedral groups 36
11.2 Triangle groups and the classical plane geometries 42
11.3 The 3 sphere as a Lie group and its finite subgroups 47
11.4 Brieskorn manifolds and Klein's theorem 50
11.5 The group PSL(2,R) and its universal cover SL(2,R) 55
11.6 Milnor's theorem for the 3 dimensional Brieskorn
manifolds. The hyperbolic case 57
11.7 Brieskorn Hamm complete intersections.
The theorem of Neumann 60
11.8 Remarks 62
x Contents
III 3 dimensioual Lie Groups and Surface Singularities
111.1 Quasi Homogeneous surface singularities 65
111.2 3 manifolds whose universal covering is a Lie group 71
111.3 Lie groups and singularities I:
quasi homogeneous singularities 75
111.4 Lie groups and singularities II: the cusps 80
111.5 Lie groups and singularities III:
the Abelian and £+(2) cases 82
111.6 A uniform picture of 3 dimensional Lie groups 85
111.7 Lie algebras and the Gorenstein property 87
111.8 Remarks 88
IV Within the Realm of the General Index Theorem
IV. 1 A review of characteristic classes 92
IV.2 On Hirzebruch's theorems about the signature
and Riemann Roch 97
IV.3 Spin and Spinc structures on 4 manifolds.
Rochlin's theorem 102
IV.4 Spin and Spin0 structures on complex surfaces.
Rochlin's theorem 105
IV.5 A review of surface singularities 110
IV.6 Gorenstein and numerically Gorenstein singularities 116
IV.7 An application of Riemann Roch: Laufer's formula 121
IV.8 Geometric genus, spinc structures and
characteristic divisors 126
IV.9 On the signature of smoothings of surface singularities . 128
IV. 10 On the Rochlin fi invariant for links
of surface singularities 131
IV. 11 Comments on new 3 manifolds invariants
and surface singularities 134
V On the Geometry and Topology of Quadrics in CPn
V.I The topology of a quadric in CPn 138
V.2 The space CPn as a double mapping cylinder 141
V.3 The orthogonal group SO(n+l,R) and
the geometry of CPn 143
V.4 Cohomogeneity 1 actions of SO(3) on CP2 and S4 148
V.5 The Arnold Kuiper Massey theorem 150
VI Real Singularities and Complex Geometry
VI.1 The space of Siegel leaves of a linear flow 157
VI.2 Real singularities and the Lopez de
Medrano Verjovsky Meersseman manifolds 163
VI.3 Real singularities and holomorphic vector fields 167
VI.4 On the topology of certain real hypersurface singularities . . . 170
Contents xi
VII Real Singularities with a Milnor Fibration
VII.1 Milnor's fibration theorem revisited 175
VII.2 The strong Milnor condition 177
VII.3 Real singularities of the Pham Brieskorn type 181
VII.4 Twisted Pham Brieskorn singularities and
the strong Milnor condition 187
VII.5 On the topology of the twisted
Pham Brieskorn singularities 191
VII.6 Stability of the Milnor conditions under perturbations 194
VII.7 Remarks and open problems 196
VIII Real Singularities and Open Book Decompositions of the 3 sphere
VIII. 1 On the resolution of embedded complex plane curves 200
VIII.2 The resolution and Seifert graphs 204
VIII.3 Seifert links and horizontal fibrations 206
VIII.4 An example 209
VIII.5 Resolution and topology of the singularities
z\z2 + z\zx =0 213
VIII.6 On singularities of the form fg 216
Bibliography 221
Index 235 |
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| series2 | Progress in mathematics Ferran Sunyer i Balaguer award winning monograph |
| spelling | On the topology of isolated singularities in analytic spaces José Seade Basel ; Boston ; Berlin Birkhäuser 2006 1 Online-Ressource (XIV, 238 S.) Ill., graph. Darst. txt rdacontent c rdamedia cr rdacarrier Progress in mathematics 241 Ferran Sunyer i Balaguer award winning monograph Literaturverz. S. 221 - 233 Isolierte Singularität (DE-588)4123453-4 gnd rswk-swf Analytischer Raum (DE-588)4001871-4 gnd rswk-swf Analytischer Raum (DE-588)4001871-4 s Isolierte Singularität (DE-588)4123453-4 s DE-604 Seade, José 1954- Sonstige (DE-588)130563072 oth Progress in mathematics 241 (DE-604)BV000004120 241 https://doi.org/10.1007/3-7643-7395-4 Verlag Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015517136&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | On the topology of isolated singularities in analytic spaces Progress in mathematics Isolierte Singularität (DE-588)4123453-4 gnd Analytischer Raum (DE-588)4001871-4 gnd |
| subject_GND | (DE-588)4123453-4 (DE-588)4001871-4 |
| title | On the topology of isolated singularities in analytic spaces |
| title_auth | On the topology of isolated singularities in analytic spaces |
| title_exact_search | On the topology of isolated singularities in analytic spaces |
| title_exact_search_txtP | On the topology of isolated singularities in analytic spaces |
| title_full | On the topology of isolated singularities in analytic spaces José Seade |
| title_fullStr | On the topology of isolated singularities in analytic spaces José Seade |
| title_full_unstemmed | On the topology of isolated singularities in analytic spaces José Seade |
| title_short | On the topology of isolated singularities in analytic spaces |
| title_sort | on the topology of isolated singularities in analytic spaces |
| topic | Isolierte Singularität (DE-588)4123453-4 gnd Analytischer Raum (DE-588)4001871-4 gnd |
| topic_facet | Isolierte Singularität Analytischer Raum |
| url | https://doi.org/10.1007/3-7643-7395-4 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015517136&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT seadejose onthetopologyofisolatedsingularitiesinanalyticspaces |