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This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex. Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Topology. --- Algebraic geometry. --- Mathematical analysis. --- Algebraic Geometry. --- Analysis. --- Singularitats (Matemàtica) --- Geometria algebraica --- Grups topològics

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This book features state-of-the-art research on singularities in geometry, topology, foliations and dynamics and provides an overview of the current state of singularity theory in these settings. Singularity theory is at the crossroad of various branches of mathematics and science in general. In recent years there have been remarkable developments, both in the theory itself and in its relations with other areas. The contributions in this volume originate from the “Workshop on Singularities in Geometry, Topology, Foliations and Dynamics”, held in Merida, Mexico, in December 2014, in celebration of José Seade’s 60th Birthday. It is intended for researchers and graduate students interested in singularity theory and its impact on other fields.

Mathematics. --- Algebraic geometry. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Functions of complex variables. --- Several Complex Variables and Analytic Spaces. --- Algebraic Geometry. --- Global Analysis and Analysis on Manifolds. --- Singularities (Mathematics) --- Geometry --- Study and teaching. --- Geometry, Algebraic --- Differential equations, partial. --- Geometry, algebraic. --- Global analysis. --- Algebraic geometry --- Partial differential equations --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Complex variables --- Elliptic functions --- Functions of real variables

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Singularitats (Matemàtica) --- Geometria algebraica --- Catàstrofes (Matemàtica) --- Esclatament (Matemàtica) --- Singularities (Mathematics) --- Geometry, Algebraic

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Ordered algebraic structures --- Algebraic geometry --- Topological groups. Lie groups --- Topology --- Geometry --- landmeetkunde --- complexe veranderlijken --- wiskunde --- geometrie --- topologie

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This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex. Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Topology. --- Algebraic geometry. --- Mathematical analysis. --- Algebraic Geometry. --- Analysis.