On the Topology of Isolated Singularities in Analytic Spaces: 241 - Rilegato

Seade, Jose

Rilegato

ISBN 10: 3764373229 ISBN 13: 9783764373221

Casa editrice: Birkhauser, 2005

Riassunto

Singularity theory stands at a cross-road of mathematics, a meeting point where manyareasofmathematicscometogether,suchasgeometry,topologyandalgebra, analysis,di?erential equations and dynamical systems, combinatoricsand number theory, to mention some of them. Thus, one who would write a book about this fascinatingtopicnecessarilyfacesthechallengeofhavingtochoosewhattoinclude and,mostdi?cult,whatnottoinclude. Acomprehensivetreatmentofsingularities would have to consist of a collection of books, which would be beyond our present scope. Hence this work does not pretend to be comprehensive of the subject, neither is it a text book with a systematic approachto singularitytheory asa core idea. Thisisrather a collectionof essaysonselected topicsaboutthe topologyand geometry of real and complex analytic spaces around their isolated singularities. I have worked in the area of singularities since the late 1970s, and during this time have had the good fortune of encountering many gems of mathematics concerningthetopologyofsingularitiesandrelatedtopics,masterpiecescreatedby greatmathematicians like Riemann, Klein and Poincar´ e,then Milnor, Hirzebruch, Thom, Mumford, Brieskorn, Atiyah, Arnold, Wall, LˆeDung ˜ Tran ´ g, Neumann, Looijenga, Teissier, and many more whose names I cannot include since the list would be too long and, even that, I would leave aside important names. My own research has always stood on the shoulders of all of them. In taking this broad approach I realize how di?cult it is to present an overall picture of the myriad of outstanding contributions in this area of mathematics during the last century, since they are scattered in very many books and research articles.

Su questo libro

Dalla quarta di copertina:

The aim of this book is to give an overview of selected topics on the topology of real and complex isolated singularities, with emphasis on its relations to other branches of geometry and topology.
The first chapters are mostly devoted to complex singularities and a myriad of results spread in a vast literature, which are presented here in a unified way, accessible to non-specialists. Among the topics are the fibration theorems of Milnor; the relation with 3-dimensional Lie groups; exotic spheres; spin structures and 3-manifold invariants; the geometry of quadrics and Arnold's theorem which states that the complex projective plane modulo conjugation is the 4-sphere.
The second part of the book studies pioneer work about real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations. In the low dimensional case these turn out to be related to fibred links in the 3-sphere defined by meromorphic functions. This provides new methods for constructing manifolds equipped with a rich geometry.
The book is largely self-contained and serves a wide audience of graduate students, mathematicians and researchers interested in geometry and topology.

Contenuti:

A Fast Trip Through the Classical Theory.- Motions in Plane Geometry and the 3-dimensional Brieskorn Manifolds.- 3-dimensional Lie Groups and Surface Singularities.- Within the Realm of the General Index Theorem.- On the Geometry and Topology of Quadrics in ??n.- Real Singularities and Complex Geometry.- Real Singularities with a Milnor Fibration.- Real Singularities and Open Book Decompositions of the 3-sphere.

Su questa edizione

• Editore: Birkhauser
• Data di pubblicazione: 2005
• ISBN 10: 3764373229
• ISBN 13: 9783764373221
• Rilegatura: Copertina rigida
• Numero di pagine: 238