Overview
- Makes accessible to non-specialists important results about real and complex singularities
- Emphasis on the relations to other branches, such as group actions, or quotiens of 3-dimensional Lie groups by discrete subgroups
- Explores pioneer work on real singularities associated to holomorphic flows and foliations, thus providing new methods for constructing manifolds equipped with a rich geometry
- Includes supplementary material: sn.pub/extras
Part of the book series: Progress in Mathematics (PM, volume 241)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: On the Topology of Isolated Singularities in Analytic Spaces
Authors: José Seade
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/3-7643-7395-4
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Basel 2006
Hardcover ISBN: 978-3-7643-7322-1Published: 18 November 2005
eBook ISBN: 978-3-7643-7395-5Published: 21 March 2006
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XIV, 238
Topics: Functions of a Complex Variable, Topological Groups, Lie Groups, Differential Geometry, Algebraic Topology