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Singular Spaces
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Book Synopsis Topology of Singular Spaces and Constructible Sheaves by : Jörg Schürmann
Download or read book Topology of Singular Spaces and Constructible Sheaves written by Jörg Schürmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the lecture notes of six courses delivered at a Cimpa Summer School in Temuco, Chile, in January 2001. Leading experts contribute with introductory articles covering a broad area in probability and its applications, such as mathematical physics and mathematics of finance. Written at graduate level, the lectures touch the latest advances on each subject, ranging from classical probability theory to modern developments. Thus the book will appeal to students, teachers and researchers working in probability theory or related fields.
Book Synopsis Differential Geometry of Singular Spaces and Reduction of Symmetry by : J. Śniatycki
Download or read book Differential Geometry of Singular Spaces and Reduction of Symmetry written by J. Śniatycki and published by Cambridge University Press. This book was released on 2013-06-13 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author illustrates the power of the theory of subcartesian differential spaces for investigating spaces with singularities. Part I gives a detailed and comprehensive presentation of the theory of differential spaces, including integration of distributions on subcartesian spaces and the structure of stratified spaces. Part II presents an effective approach to the reduction of symmetries. Concrete applications covered in the text include reduction of symmetries of Hamiltonian systems, non-holonomically constrained systems, Dirac structures, and the commutation of quantization with reduction for a proper action of the symmetry group. With each application the author provides an introduction to the field in which relevant problems occur. This book will appeal to researchers and graduate students in mathematics and engineering.
Book Synopsis Spinors on Singular Spaces and the Topology of Causal Fermion Systems by : Felix Finster
Download or read book Spinors on Singular Spaces and the Topology of Causal Fermion Systems written by Felix Finster and published by American Mathematical Soc.. This book was released on 2019-06-10 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures are introduced and analyzed. The connection to the spin condition in differential topology is worked out. The constructions are illustrated by many simple examples such as the Euclidean plane, the two-dimensional Minkowski space, a conical singularity, a lattice system as well as the curvature singularity of the Schwarzschild space-time. As further examples, it is shown how complex and Kähler structures can be encoded in Riemannian fermion systems.
Book Synopsis Categorical Framework for the Study of Singular Spaces by : William Fulton
Download or read book Categorical Framework for the Study of Singular Spaces written by William Fulton and published by American Mathematical Soc.. This book was released on 1981 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: In several areas of geometry and topology it has become apparent that the traditional covariant and contravariant functors are insufficient, particularly for dealing with geometric questions about singular spaces. We develop here a new formalism called bivariant theories. These are simultaneous generalizations of covariant group valued "homology-like" theories and contravariant ring valued "cohomology-like" theories. Most traditional pairs of covariant and contravariant theories turn out to extend to bivariant theories. A bivariant theory assigns a group not to an object but to a morphism of the original category; it has products compatible with composition of morphisms. We will also define transformations from one bivariant theory to another, called Grothendieck transformations, which generalize ordinary natural transformations. A number of standard natural transformations turn out to extend to Grothendieck transformations, and this extension has deep consequences.
Book Synopsis Singular Spaces by : Jo Farb Hernandez
Download or read book Singular Spaces written by Jo Farb Hernandez and published by Marquand Books. This book was released on 2013 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published by leading outsider art imprint Raw Vision, Singular Spaces is a groundbreaking survey of art environments created by self-taught artists from across Spain. The book introduces and examines 45 artists and their idiosyncratic sculptures, gardens and buildings, most of which have never been published. The sites are developed organically, without formal architectural or engineering plans; they are at once evolving and complete. Often highly fanciful and quixotic, the work is frequently characterized by incongruous juxtapositions, an approach that appears impulsive and spontaneous. Director of the organization SPACES (Saving and Preserving Arts and Cultural Environments), Jo Farb Hernández, combines detailed case studies of the artists and their work with contextualized historical and theoretical references to art history, anthropology, architecture, Spanish area studies and folklore. Breaking down the standard compartmentalization of genres, she reveals how most creators of art environments, who are building within their own personal spaces, fuse their creations with their daily lives.
Book Synopsis Rigidity Results for Singular Spaces by : Jean-François R. Lafont
Download or read book Rigidity Results for Singular Spaces written by Jean-François R. Lafont and published by . This book was released on 2002 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topology of Stratified Spaces by : Greg Friedman
Download or read book Topology of Stratified Spaces written by Greg Friedman and published by Cambridge University Press. This book was released on 2011-03-28 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.
Book Synopsis Analytic and Geometric Study of Stratified Spaces by : Markus J. Pflaum
Download or read book Analytic and Geometric Study of Stratified Spaces written by Markus J. Pflaum and published by Springer. This book was released on 2003-07-01 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an introduction to stratification theory leading the reader up to modern research topics in the field. The first part presents the basics of stratification theory, in particular the Whitney conditions and Mather's control theory, and introduces the notion of a smooth structure. Moreover, it explains how one can use smooth structures to transfer differential geometric and analytic methods from the arena of manifolds to stratified spaces. In the second part the methods established in the first part are applied to particular classes of stratified spaces like for example orbit spaces. Then a new de Rham theory for stratified spaces is established and finally the Hochschild (co)homology theory of smooth functions on certain classes of stratified spaces is studied. The book should be accessible to readers acquainted with the basics of topology, analysis and differential geometry.
Book Synopsis Solipsism, Physical Things and Personal Perceptual Space by : Safak Ural
Download or read book Solipsism, Physical Things and Personal Perceptual Space written by Safak Ural and published by Vernon Press. This book was released on 2019-09-30 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solipsism indicates an epistemological position that denies the existence of ‘others’ by asserting that the ‘self’ is the only thing that can be known to exist. For sophist philosophers, the belief that “we can not know anything, and even if we do so, we cannot communicate it” is central to this theory. However, until now there has been little academic scholarship that has tried to provide answers to the pressing issues raised by solipsism. In Solipsist Ontology: Physical Things and Personal Perceptual Space, Ural aims to redefine solipsism by analyzing and elaborating on traditional philosophical problems, such as empiricism and rationalism, as well as discussing problems of language, communication, and meaning. Ural reveals where solipsism has been previously ignored, pseudo-problems have arisen that disguise the sources of the problems with prejudices that concern the philosophical problems in question. Notably, many current, as well as traditional problems of ontology, epistemology, and language are bound up in discourses of solipsism. Ural argues that discarding solipsism as a philosophical discourse hinders new interpretations of traditional philosophical thought. This book offers a fresh perspective to solipsism by defining it in relation to concepts such as ‘physical things,’ ‘personal perceptual space’ and ‘identity.’ Importantly, Ural proposes that an understanding of ‘identity’ is not necessary in order to redefine solipsism. By building a logical system that fashions communication and solipsism as interrelated, it is possible to reject ‘identity’ as a useless concept and thus overcome the classic solipsist dilemma of “we are not able to communicate.” This original piece of research is an important and timely contribution to the field of philosophy that will be of great interest to teachers, researchers, and students.
Download or read book Singularity Theory written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Physiologia written by Dennis Des Chene and published by Cornell University Press. This book was released on 2000 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Natural Change -- 2. Motus, Potentia, Actus -- 3. Form, Privation, and Substance -- 4. Matter, Quantity, and Figure -- 5. The Structure of Physical Substance -- 6. Finality and Final Causes -- 7. Nature and Counternature -- 8. Motion and Its Causes -- 9. Parts of Matter -- 10. World without Ends.
Book Synopsis K-theory and Noncommutative Geometry by : Guillermo Cortiñas
Download or read book K-theory and Noncommutative Geometry written by Guillermo Cortiñas and published by European Mathematical Society. This book was released on 2008 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its inception 50 years ago, K-theory has been a tool for understanding a wide-ranging family of mathematical structures and their invariants: topological spaces, rings, algebraic varieties and operator algebras are the dominant examples. The invariants range from characteristic classes in cohomology, determinants of matrices, Chow groups of varieties, as well as traces and indices of elliptic operators. Thus K-theory is notable for its connections with other branches of mathematics. Noncommutative geometry develops tools which allow one to think of noncommutative algebras in the same footing as commutative ones: as algebras of functions on (noncommutative) spaces. The algebras in question come from problems in various areas of mathematics and mathematical physics; typical examples include algebras of pseudodifferential operators, group algebras, and other algebras arising from quantum field theory. To study noncommutative geometric problems one considers invariants of the relevant noncommutative algebras. These invariants include algebraic and topological K-theory, and also cyclic homology, discovered independently by Alain Connes and Boris Tsygan, which can be regarded both as a noncommutative version of de Rham cohomology and as an additive version of K-theory. There are primary and secondary Chern characters which pass from K-theory to cyclic homology. These characters are relevant both to noncommutative and commutative problems and have applications ranging from index theorems to the detection of singularities of commutative algebraic varieties. The contributions to this volume represent this range of connections between K-theory, noncommmutative geometry, and other branches of mathematics.
Book Synopsis Singularity Theory by : Denis Chniot
Download or read book Singularity Theory written by Denis Chniot and published by World Scientific. This book was released on 2007 with total page 1083 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory.The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.
Book Synopsis Collection of Papers on Geometry, Analysis and Mathematical Physics by : Daqian Li
Download or read book Collection of Papers on Geometry, Analysis and Mathematical Physics written by Daqian Li and published by World Scientific. This book was released on 1997 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is published in honor of Professor Gu Chaohao, a renowned mathematician and member of the Chinese Academy of Sciences, on the occasion of his 70th birthday and his 50th year of educational work. The subjects covered by this collection are closely related to differential geometry, partial differential equations and mathematical physics ? the major areas in which Professor Gu has received notable achievements. Many distinguished mathematicians all over the world contributed their papers to this collection. This collection also consists of ?Gu Chaohao and I? written by C N Yang, ?The academic career and accomplishment of Professor Gu Chaohao? by T T Li and ?List of publications of Professor Gu Chaohao?.
Book Synopsis Finite Geometry and Combinatorial Applications by : Simeon Ball
Download or read book Finite Geometry and Combinatorial Applications written by Simeon Ball and published by Cambridge University Press. This book was released on 2015-07-02 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level introduction to finite geometry and its applications to other areas of combinatorics.
Book Synopsis Topological Invariants of Stratified Spaces by : Markus Banagl
Download or read book Topological Invariants of Stratified Spaces written by Markus Banagl and published by Springer Science & Business Media. This book was released on 2007-02-16 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this book is the restoration of Poincaré duality on stratified singular spaces by using Verdier-self-dual sheaves such as the prototypical intersection chain sheaf on a complex variety. Highlights include complete and detailed proofs of decomposition theorems for self-dual sheaves, explanation of methods for computing twisted characteristic classes and an introduction to the author's theory of non-Witt spaces and Lagrangian structures.
Book Synopsis Extending Intersection Homology Type Invariants to Non-Witt Spaces by : Markus Banagl
Download or read book Extending Intersection Homology Type Invariants to Non-Witt Spaces written by Markus Banagl and published by American Mathematical Soc.. This book was released on 2002 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intersection homology theory provides a way to obtain generalized Poincare duality, as well as a signature and characteristic classes, for singular spaces. For this to work, one has had to assume however that the space satisfies the so-called Witt condition. We extend this approach to constructing invariants to spaces more general than Witt spaces. We present an algebraic framework for extending generalized Poincare duality and intersection homology to singular spaces $X$ not necessarily Witt. The initial step in this program is to define the category $SD(X)$ of complexes of sheaves suitable for studying intersection homology type invariants on non-Witt spaces. The objects in this category can be shown to be the closest possible self-dual 'approximation' to intersection homology sheaves.It is therefore desirable to understand the structure of such self-dual sheaves and to isolate the minimal data necessary to construct them. As the main tool in this analysis we introduce the notion of a Lagrangian structure (related to the familiar notion of Lagrangian submodules for $(-1)^k$-Hermitian forms, as in surgery theory). We demonstrate that every complex in $SD(X)$ has naturally associated Lagrangian structures and conversely, that Lagrangian structures serve as the natural building blocks for objects in $SD(X).Our main result asserts that there is in fact an equivalence of categories between $SD(X)$ and a twisted product of categories of Lagrangian structures. This may be viewed as a Postnikov system for $SD(X)$ whose fibers are categories of Lagrangian structures. The question arises as to which varieties possess Lagrangian structures. To begin to answer that, we define the model-class of varieties with an ordered resolution and use block bundles to describe the geometry of such spaces. Our main result concerning these is that they have associated preferred Lagrangian structures, and hence self-dual generalized intersection homology sheaves.
