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Handbook of Geometry and Topology of Singularities III (Hardcover, 1st ed. 2022)
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Handbook of Geometry and Topology of Singularities III (Hardcover, 1st ed. 2022)
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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.
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