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Intersection Spaces Spatial Homology Truncation And String Theory


Intersection Spaces Spatial Homology Truncation And String Theory
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Intersection Spaces Spatial Homology Truncation And String Theory


Intersection Spaces Spatial Homology Truncation And String Theory
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Author : Markus Banagl
language : en
Publisher: Springer
Release Date : 2010-06-16

Intersection Spaces Spatial Homology Truncation And String Theory written by Markus Banagl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-16 with Mathematics categories.


Intersection cohomology assigns groups which satisfy a generalized form of Poincaré duality over the rationals to a stratified singular space. This monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose ordinary rational homology satisfies generalized Poincaré duality. The cornerstone of the method is a process of spatial homology truncation, whose functoriality properties are analyzed in detail. The material on truncation is autonomous and may be of independent interest tohomotopy theorists. The cohomology of intersection spaces is not isomorphic to intersection cohomology and possesses algebraic features such as perversity-internal cup-products and cohomology operations that are not generally available for intersection cohomology. A mirror-symmetric interpretation, as well as applications to string theory concerning massless D-branes arising in type IIB theory during a Calabi-Yau conifold transition, are discussed.



Singular Intersection Homology


Singular Intersection Homology
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Author : Greg Friedman
language : en
Publisher: Cambridge University Press
Release Date : 2020-09-24

Singular Intersection Homology 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 2020-09-24 with Mathematics categories.


The first expository book-length introduction to intersection homology from the viewpoint of singular and piecewise linear chains.



Intersection Cohomology Simplicial Blow Up And Rational Homotopy


Intersection Cohomology Simplicial Blow Up And Rational Homotopy
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Author : David Chataur
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-09

Intersection Cohomology Simplicial Blow Up And Rational Homotopy written by David Chataur 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 2018-08-09 with Mathematics categories.


Let X be a pseudomanifold. In this text, the authors use a simplicial blow-up to define a cochain complex whose cohomology with coefficients in a field, is isomorphic to the intersection cohomology of X, introduced by M. Goresky and R. MacPherson. The authors do it simplicially in the setting of a filtered version of face sets, also called simplicial sets without degeneracies, in the sense of C. P. Rourke and B. J. Sanderson. They define perverse local systems over filtered face sets and intersection cohomology with coefficients in a perverse local system. In particular, as announced above when X is a pseudomanifold, the authors get a perverse local system of cochains quasi-isomorphic to the intersection cochains of Goresky and MacPherson, over a field. We show also that these two complexes of cochains are quasi-isomorphic to a filtered version of Sullivan's differential forms over the field Q. In a second step, they use these forms to extend Sullivan's presentation of rational homotopy type to intersection cohomology.



Handbook Of Geometry And Topology Of Singularities Ii


Handbook Of Geometry And Topology Of Singularities Ii
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Author : José Luis Cisneros-Molina
language : en
Publisher: Springer Nature
Release Date : 2021-11-01

Handbook Of Geometry And Topology Of Singularities Ii 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 2021-11-01 with Mathematics categories.


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 Of Stratified Spaces


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.



Lebesgue And Sobolev Spaces With Variable Exponents


Lebesgue And Sobolev Spaces With Variable Exponents
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Author : Lars Diening
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-31

Lebesgue And Sobolev Spaces With Variable Exponents written by Lars Diening 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 2011-03-31 with Mathematics categories.


The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.



Calabi Yau Manifolds A Bestiary For Physicists 2nd Edition


Calabi Yau Manifolds A Bestiary For Physicists 2nd Edition
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Author : Tristan Hubsch
language : en
Publisher: World Scientific
Release Date : 2024-12-17

Calabi Yau Manifolds A Bestiary For Physicists 2nd Edition written by Tristan Hubsch and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-17 with Science categories.


Calabi-Yau spaces are complex spaces with a vanishing first Chern class, or, equivalently, with a trivial canonical bundle (sheaf), so they admit a Ricci-flat Kähler metric that satisfies the vacuum Einstein equations. Used to construct possibly realistic (super)string models, they are being studied vigorously by physicists and mathematicians alike. Calabi-Yau spaces have also turned up in computations of probability amplitudes in quantum field theory. This book collects and reviews relevant results on several major techniques of (1) constructing such spaces and (2) computing physically relevant quantities such as spectra of massless fields and their Yukawa interactions. These are amended by (3) stringy corrections and (4) results about the moduli space and its geometry, including a preliminary discussion of the still conjectural universal deformation space. It also contains a lexicon of assorted terms and important results and theorems, which can be used independently.The first edition of Calabi-Yau Manifolds: A Bestiary for Physicists was the first systematic book covering Calabi-Yau spaces, related mathematics, and their application in physics. Thirty years on, this new edition explores the intense development in the field since 1992, providing an additional 400 references. It also addresses advances in machine learning and other computer-aided methods that have recently made physically relevant computations feasible, opened new avenues in the field, and begun to deliver concretely on the now 40-year-old promise of string theory. The presentation of ideas, results, and computational methods is complemented by detailed models and sample computations throughout. This second edition also contains a new closing section, outlining the staggering advances of the past three decades and providing suggestions for future reading.



Blow Up Theories For Semilinear Parabolic Equations


Blow Up Theories For Semilinear Parabolic Equations
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Author : Bei Hu
language : en
Publisher: Springer
Release Date : 2011-03-17

Blow Up Theories For Semilinear Parabolic Equations written by Bei Hu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-17 with Mathematics categories.


There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.



L Vy Matters I


L Vy Matters I
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Author : Thomas Duquesne
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-05

L Vy Matters I written by Thomas Duquesne 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 2010-09-05 with Mathematics categories.


Focusing on the breadth of the topic, this volume explores Lévy processes and applications, and presents the state-of-the-art in this evolving area of study. These expository articles help to disseminate important theoretical and applied research to those studying the field.



Topological Complexity Of Smooth Random Functions


Topological Complexity Of Smooth Random Functions
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Author : Robert Adler
language : en
Publisher: Springer
Release Date : 2011-05-16

Topological Complexity Of Smooth Random Functions written by Robert Adler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-16 with Mathematics categories.


These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.