Topology of singular fibers of differentiable maps
The volume develops a thorough theory of singular fibers of generic differentiable maps. This is the first work that establishes the foundational framework of the global study of singular differentiable maps of negative codimension from the viewpoint of differential topology. The book contains not only a general theory, but also some explicit examples together with a number of very concrete applications. This is a very interesting subject in differential topology, since it shows a beautiful interplay between the usual theory of singularities of differentiable maps and the geometric topology of manifolds. TOC:Part I. Classification of Singular Fibers: Preliminaries.- Singular Fibers of Morse Functions on Surfaces.- Classification of Singular Fibers.- Co-existence of Singular Fibers.- Euler Characteristic of the Source 4-Manifold.- Examples of Stable Maps of 4-Manifolds.- Part II. Universal Complex of Singular Fibers: Generalities.- Universal Complex of Singular Fibers.- Stable Maps of 4-Manifolds into 3-Manifolds.- Co-orientable Singular Fibers.- Homomorphism Induced by a Thom Map.-Cobordism Invariance.- Cobordism of Maps with Prescribed Local Singularities.- Examples of Cobordism Invariants.- Part III. Epilogue: Applications.- Further Developments.- References.- List of Symbols.- Index
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- ISBN
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9783540230212
3540230211
- Dimensions
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24 cm
- Extent
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X, 145 S.
- Language
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Englisch
- Notes
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graph. Darst.
Literaturverz. S. 131 - 134
- Bibliographic citation
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Lecture notes in mathematics ; Vol. 1854
- Classification
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Mathematik
- Keyword
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Topologische Mannigfaltigkeit
Differenzierbare Abbildung
Singularität
Faser
Differentialtopologie
- Event
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Veröffentlichung
- (where)
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Berlin, Heidelberg, New York
- (who)
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Springer
- (when)
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2004
- Creator
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Saeki, Osamu
- Table of contents
- Rights
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Bei diesem Objekt liegt nur das Inhaltsverzeichnis digital vor. Der Zugriff darauf ist unbeschränkt möglich.
- Last update
-
11.03.2025, 12:24 PM CET
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Saeki, Osamu
- Springer
Time of origin
- 2004
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Performance and storage requirements of topology-conserving maps for robot manipulator control
Intrinsic Dimensionality Estimation with Optimally Topology Preserving Maps
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Singular elliptic fibers at codimension two and representation theory of matter in F-theory models, I
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Topology of surfaces
Singular fibers of Hitchin systems
Topology of singular spaces and constructible sheaves
Fibers of rational maps and Jacobian matrices
Exponential maps with escaping singular orbits
Performance and storage requirements of topology-conserving maps for robot manipulator control
Intrinsic Dimensionality Estimation with Optimally Topology Preserving Maps
Grassmannians and Gauss maps in piecewise-linear topology
Stable maps and singular curves on K3 surfaces
Singular elliptic fibers at codimension two and representation theory of matter in F-theory models, II
Singular elliptic fibers at codimension two and representation theory of matter in F-theory models, I
Topology of violence