## Le Cycles and Hypersurface SingularitiesThis 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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### Contents

Preface Table of Contents V | 1 |

Definitions and Basic Properties | 8 |

Elementary Examples | 31 |

Copyright | |

9 other sections not shown

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Algebraic aligned Analysis analytic analytic function apply arrangement assume calculate Chapter characteristic complex component conclude condition consider constant contained coordinates Corollary critical locus curve defined definition denote diffeomorphic dimension dimo dimp Editors equal Example exists fibration Finally finite fixed follows formula germs give given Groups Hence homology homotopy homotopy-equivalence hyperplane hypersurface implies inclusion independent inductive Lê cycles Lê numbers Lemma linear Math Methods Milnor fibre Milnor number Moreover multiplicity non-zero Note obtain one-dimensional open neighborhood origin polar polynomial prepolar Problems Proceedings Proof Proposition prove purely Remark respect result satisfies scheme sequence sheaf singularity smooth space strata stratification stratum subset Suppose taking Theorem Theory Topology transversely intersects universal V(zo varieties VIII Whitney wish