Intersection Spaces Spatial Homology Truncation And String Theory PDF Download
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| Author | : Markus Banagl |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 237 |
| Release | : 2010-07-08 |
| Genre | : Mathematics |
| ISBN | : 3642125883 |
Download Intersection Spaces, Spatial Homology Truncation, and String Theory Book in PDF, ePub and Kindle
The present 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.
| Author | : Markus Banagl |
| Publisher | : Springer |
| Total Pages | : 237 |
| Release | : 2010-06-16 |
| Genre | : Mathematics |
| ISBN | : 3642125891 |
Download Intersection Spaces, Spatial Homology Truncation, and String Theory Book in PDF, ePub and Kindle
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.
| Author | : Greg Friedman |
| Publisher | : Cambridge University Press |
| Total Pages | : 824 |
| Release | : 2020-09-24 |
| Genre | : Mathematics |
| ISBN | : 1108895360 |
Download Singular Intersection Homology Book in PDF, ePub and Kindle
Intersection homology is a version of homology theory that extends Poincaré duality and its applications to stratified spaces, such as singular varieties. This is the first comprehensive expository book-length introduction to intersection homology from the viewpoint of singular and piecewise-linear chains. Recent breakthroughs have made this approach viable by providing intersection homology and cohomology versions of all the standard tools in the homology tool box, making the subject readily accessible to graduate students and researchers in topology as well as researchers from other fields. This text includes both new research material and new proofs of previously-known results in intersection homology, as well as treatments of many classical topics in algebraic and manifold topology. Written in a detailed but expository style, this book is suitable as an introduction to intersection homology or as a thorough reference.
| Author | : José Luis Cisneros-Molina |
| Publisher | : Springer Nature |
| Total Pages | : 581 |
| Release | : 2021-11-01 |
| Genre | : Mathematics |
| ISBN | : 3030780244 |
Download Handbook of Geometry and Topology of Singularities II Book in PDF, ePub and Kindle
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.
| Author | : Greg Friedman |
| Publisher | : Cambridge University Press |
| Total Pages | : 491 |
| Release | : 2011-03-28 |
| Genre | : Mathematics |
| ISBN | : 052119167X |
Download Topology of Stratified Spaces Book in PDF, ePub and Kindle
This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.
| Author | : David Chataur |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 108 |
| Release | : 2018-08-09 |
| Genre | : |
| ISBN | : 1470428873 |
Download Intersection Cohomology, Simplicial Blow-Up and Rational Homotopy Book in PDF, ePub and Kindle
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.
| Author | : Lars Diening |
| Publisher | : Springer |
| Total Pages | : 516 |
| Release | : 2011-03-29 |
| Genre | : Mathematics |
| ISBN | : 3642183638 |
Download Lebesgue and Sobolev Spaces with Variable Exponents Book in PDF, ePub and Kindle
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.
| Author | : Bei Hu |
| Publisher | : Springer |
| Total Pages | : 137 |
| Release | : 2011-03-17 |
| Genre | : Mathematics |
| ISBN | : 364218460X |
Download Blow-up Theories for Semilinear Parabolic Equations Book in PDF, ePub and Kindle
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.
| Author | : Thomas Duquesne |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 216 |
| Release | : 2010-09-05 |
| Genre | : Mathematics |
| ISBN | : 3642140068 |
Download Lévy Matters I Book in PDF, ePub and Kindle
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.
| Author | : Robert Adler |
| Publisher | : Springer |
| Total Pages | : 135 |
| Release | : 2011-05-16 |
| Genre | : Mathematics |
| ISBN | : 3642195806 |
Download Topological Complexity of Smooth Random Functions Book in PDF, ePub and Kindle
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.
