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The Geometry of Topological Stability : London Mathematical Society Monographs - Andrew A. du Plessis

The Geometry of Topological Stability

London Mathematical Society Monographs


Published: 7th December 1995
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The aim of this book is to give necessary and sufficient conditions for a C oo map to be C 0-stable; the aim is achieved in a wide range of dimensions via a detailed study of the geometry and topology of many classes of "generic" singularities. The methods developed for examining the topology and geometry use results from many areas of mathematics - geometric topology, stratification theory, algebraic topology, algebraic geometry, commutative algebra...- and further progress will doubtless be made from the application of deeper results from these areas. Conversely, it is to be hoped that the description of the behaviour of generic singularities will also have interesting consequences for these areas of mathematics, which are those with most interaction with singularity theory. The book describes original research; essentially none of its results has previously appeared elsewhere, either in scientific articles or in books. This book is intended for research mathematicians in singularity theory and in selected areas of geometric topology, stratification theory, algebraic geometry, commutative algebra.

`In judging the importance of the present work in the context of stability of smooth maps, it cannot be easily overestimated. It guides the reader through a maze of complicated new results including proofs at the center of manifold theory.' Zentralblatt fuer Mathematik 870/97

Part I: Prolegomena to Stability Theory General introduction 1: Review of stability theory 2: Proper maps and function space topologies 3: Various notions of stability Part II: Necessary Conditions 4: Disruptive germ classes 5: Necessary conditions for topological stability 6: Stable topological invariance of u-constant strata 7: Stable topological type of finite map-germs Part III: Sufficient Conditions 8: A sufficient condition for strong topological stability 9: Algebraic criteria for civilization 10: Calculations of instability loci Part IV: Conclusion 11: Necessary and sufficient conditions for stability Problems References Index

ISBN: 9780198535881
ISBN-10: 0198535880
Series: London Mathematical Society Monographs
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 580
Published: 7th December 1995
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 24.1 x 16.2  x 3.7
Weight (kg): 1.0