Handbook of geometry and topology of singularities
Author(s)
Bibliographic Information
Handbook of geometry and topology of singularities
Springer, c2022
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- Other Title
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Handbook of geometry and topology of singularities III
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Note
Includes bibliographical references and index
Description and Table of Contents
Description
This is the third volume of the Handbook of 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 various important aspects of singularity theory. Some of these complement topics previously explored in volumes I and II, such as, for instance, Zariski's equisingularity, the interplay between isolated complex surface singularities and 3-manifold theory, stratified Morse theory, constructible sheaves, the topology of the non-critical levels of holomorphic functions, and intersection cohomology. Other chapters bring in new subjects, such as the Thom-Mather theory for maps, characteristic classes for singular varieties, mixed Hodge structures, residues in complex analytic varieties, nearby and vanishing cycles, and more.
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.
Table of Contents
1 Maria Aparecida Soares Ruas, Old and new results on density of stable mappings.- 2 David Mond and Juan Jose Nuno-Ballesteros, Singularities of mappings.- 3 Javier Fernandez de Bobadilla, Topological equisingularity: old problems from a new perspective (With an appendix by G. -M. Greuel and G. Pfister on Singular).- 4 Andras Nemethi, Surface singularities, Seiberg-Witten invariants of their links and lattice cohomology.- 5 Jean-Paul Brasselet, Characteristic classes.- 6 Paolo Aluffi, Segre classes and invariants of singular varieties.- 7 Roberto Callejas-Bedregal, Michelle F. Z. Morgado and Jose Seade, Milnor number and Chern classes for singular varieties: an Introduction.- 8 Tatsuo Suwa, Residues and hyperfunctions.- 9 Joseph Steenbrink, Mixed Hodge structures applied to singularities.- 10 Laurentiu G. Maxim and Joerg Schurmann, Constructible sheaf complexes in complex geometry and Applications.
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