Lê Cycles and Hypersurface Singularities

David B. Massey (auth.)9783540603955, 3-540-60395-6

This book describes and gives applications of an important new tool in the study of complex analytic hypersurface singularities: the Lê cycles of the hypersurface. The Lê cycles and their multiplicities – the Lê numbers – provide effectively calculable data which generalizes the Milnor number of an isolated singularity to the case of singularities of arbitrary dimension. The Lê numbers control many topological and geometric properties of such non-isolated hypersurface singularities. This book is intended for graduate students and researchers interested in complex analytic singularities.

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Table of contents :
Introduction….Pages 1-7
Definitions and basic properties….Pages 8-30
Elementary examples….Pages 31-36
A handle decomposition of the milnor fibre….Pages 37-41
Generalized Lê-Iomdine formulas….Pages 42-60
Lê numbers and hyperplane arrangements….Pages 61-67
Thom’s a f condition….Pages 68-74
Aligned singularities….Pages 75-80
Suspending singularities….Pages 81-85
Constancy of the Milnor fibrations….Pages 86-91
Other characterizations of the Lê cycles….Pages 92-104