Topology Of Singular Spaces And Constructible Sheaves
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Topology Of Singular Spaces And Constructible Sheaves
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Author : Jörg Schürmann
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Topology Of Singular Spaces And Constructible Sheaves written by Jörg Schürmann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Assuming that the reader is familiar with sheaf theory, the book gives a self-contained introduction to the theory of constructible sheaves related to many kinds of singular spaces, such as cell complexes, triangulated spaces, semialgebraic and subanalytic sets, complex algebraic or analytic sets, stratified spaces, and quotient spaces. The relation to the underlying geometrical ideas are worked out in detail, together with many applications to the topology of such spaces. All chapters have their own detailed introduction, containing the main results and definitions, illustrated in simple terms by a number of examples. The technical details of the proof are postponed to later sections, since these are not needed for the applications.
Topology Of Stratified Spaces
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Author : Greg Friedman
language : en
Publisher: Cambridge University Press
Release Date : 2011-03-28
Topology Of Stratified Spaces written by Greg Friedman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-28 with Mathematics categories.
This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.
Sheaves In Topology
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Author : Alexandru Dimca
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Sheaves In Topology written by Alexandru Dimca and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds. This introduction to the subject can be regarded as a textbook on modern algebraic topology, treating the cohomology of spaces with sheaf (as opposed to constant) coefficients. The author helps readers progress quickly from the basic theory to current research questions, thoroughly supported along the way by examples and exercises.
Sheaves In Topology
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Author : Alexandru Dimca
language : en
Publisher:
Release Date : 2011-03-30
Sheaves In Topology written by Alexandru Dimca and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-30 with categories.
A Panorama Of Singularities
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Author : Francisco-Jesús Castro-Jiménez
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-01-13
A Panorama Of Singularities written by Francisco-Jesús Castro-Jiménez and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-13 with Education categories.
This volume contains the proceedings of the conference A Panorama on Singular Varieties, celebrating the 70th birthday of Lê Dũng Tráng, held from February 7–10, 2017, at the University of Seville, IMUS, Seville, Spain. The articles cover a wide range of topics in the study of singularities and should be of great value to graduate students and research faculty who have a basic background in the theory of singularities.
Global Aspects Of Complex Geometry
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Author : Fabrizio Catanese
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-29
Global Aspects Of Complex Geometry written by Fabrizio Catanese and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-29 with Mathematics categories.
This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kähler geometry, and group actions to Hodge theory and characteristic p-geometry. Written by established experts this book will be a must for mathematicians working in Complex Geometry
Singularities In Geometry And Topology
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Author : Jean-Paul Brasselet
language : en
Publisher: World Scientific
Release Date : 2007
Singularities In Geometry And Topology written by Jean-Paul Brasselet and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology. The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.
Isomorphisms Between H1 Spaces
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Author : Paul F.X. Müller
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-04-20
Isomorphisms Between H1 Spaces written by Paul F.X. Müller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-20 with Mathematics categories.
This book gives a thorough and self contained presentation of H1, its known isomorphic invariants and a complete classification of H1 on spaces of homogeneous type. The necessary background is developed from scratch. This includes a detailed discussion of the Haar system, together with the operators that can be built from it. Complete proofs are given for the classical martingale inequalities, and for large deviation inequalities. Complex interpolation is treated. Througout, special attention is given to the combinatorial methods developed in the field. An entire chapter is devoted to study the combinatorics of coloured dyadic Intervals.
Handbook Of Geometry And Topology Of Singularities Vii
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Author : José Luis Cisneros-Molina
language : en
Publisher: Springer Nature
Release Date : 2025-03-01
Handbook Of Geometry And Topology Of Singularities Vii written by José Luis Cisneros-Molina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-01 with Mathematics categories.
This is the seventh 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 fourteen chapters that provide an in-depth and reader-friendly introduction to various important aspects of singularity theory. The volume begins with an outstanding exposition on Jim Damon’s contributions to singularity theory and its applications. Jim passed away in 2022 and he was one of the greatest mathematicians of recent times, having made remarkable contributions to singularity theory and its applications, mostly to medical image computing. The next chapter focuses on the singularities of real functions and their bifurcation sets. Then, we look at the perturbation theory of polynomials and linear operators, complex analytic frontal singularities, the global singularity theory of differentiable maps, and the singularities of holomorphic functions from a global point of view. The volume continues with an overview of new tools in singularity theory that spring from symplectic geometry and Floer-type homology theories. Then, it looks at the derivation of Lie algebras of isolated singularities and the three-dimensional rational isolated complete intersection singularities, as well as recent developments in algebraic K-stability and the stable degeneration conjecture. This volume also contains an interesting survey on V-filtrations, a theory began by Malgrange and Kashiwara that can be used to study nearby and vanishing cycle functors and introduced by Deligne. Then, we present a panoramic view of the Hodge, toric, and motivic methods in the study of Milnor fibers in singularity theory, both from local and global points of view. The Monodromy conjecture is also explained; this is a longstanding open problem in singularity theory that lies at the crossroads of number theory, algebra, analysis, geometry, and topology. This volume closes with recent developments in the study of the algebraic complexity of optimization problems in applied algebraic geometry and algebraic statistics. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
Real And Complex Singularities
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Author : M. Manoel
language : en
Publisher: Cambridge University Press
Release Date : 2010-10-07
Real And Complex Singularities written by M. Manoel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-07 with Mathematics categories.
The biennial meetings at São Carlos have helped create a worldwide community of experts and young researchers working on singularity theory, with a special focus on applications to topics in both pure and applied mathematics. This volume brings together surveys and recent work from the tenth São Carlos meeting.