On the Topology of Isolated Singularities in Analytic Spaces

  • José Seade

Part of the Progress in Mathematics book series (PM, volume 241)

About this book

Introduction

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.

Keywords

Analytic functions Complex analysis Meromorphic function Singularities Topology manifold open book open book decompositions

Authors and affiliations

  • José Seade
    • 1
  1. 1.Instituto de Matemáticas, Unidad CuernavacaUniversidad Nacional Autónoma de México (UNAM)Cuernavaca, MorelosMéxico

Bibliographic information

  • DOI https://doi.org/10.1007/3-7643-7395-4
  • Copyright Information Birkhäuser Verlag 2006
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-7643-7322-1
  • Online ISBN 978-3-7643-7395-5
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • About this book