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This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory. 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. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject. This is the first volume in a series which 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. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Algebraic geometry. --- Topological groups. --- Lie groups. --- Functions of complex variables. --- Projective geometry. --- Topology. --- Algebraic Geometry. --- Topological Groups, Lie Groups. --- Several Complex Variables and Analytic Spaces. --- Projective Geometry. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Projective geometry --- Geometry, Modern --- Complex variables --- Elliptic functions --- Functions of real variables --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Algebraic geometry --- Geometry, Algebraic. --- Singularities (Mathematics) --- Geometry, Algebraic --- Lie groups --- Functions of complex variables --- Geometry, Projective --- Topology --- Topological Groups and Lie Groups.

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This is the second volume of the Handbook of the Geometry and Topology of Singularities, a series which 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 ten chapters which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory and related topics. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and 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 --- Geometry --- geometrie --- topologie

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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