Synthetic Differential Topology

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Synthetic Differential Topology

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Author : Marta Bunge
Publisher : Cambridge University Press
ISBN 13 : 1108692206
Total Pages : 234 pages
Book Rating : 4.1/5 (86 download)

Book Synopsis Synthetic Differential Topology by : Marta Bunge

Download or read book Synthetic Differential Topology written by Marta Bunge and published by Cambridge University Press. This book was released on 2018-03-29 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book formally introduces synthetic differential topology, a natural extension of the theory of synthetic differential geometry which captures classical concepts of differential geometry and topology by means of the rich categorical structure of a necessarily non-Boolean topos and of the systematic use of logical infinitesimal objects in it. Beginning with an introduction to those parts of topos theory and synthetic differential geometry necessary for the remainder, this clear and comprehensive text covers the general theory of synthetic differential topology and several applications of it to classical mathematics, including the calculus of variations, Mather's theorem, and Morse theory on the classification of singularities. The book represents the state of the art in synthetic differential topology and will be of interest to researchers in topos theory and to mathematicians interested in the categorical foundations of differential geometry and topology.

Basic Concepts of Synthetic Differential Geometry

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Author : R. Lavendhomme
Publisher : Springer Science & Business Media
ISBN 13 : 1475745885
Total Pages : 331 pages
Book Rating : 4.4/5 (757 download)

Book Synopsis Basic Concepts of Synthetic Differential Geometry by : R. Lavendhomme

Download or read book Basic Concepts of Synthetic Differential Geometry written by R. Lavendhomme and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting at an introductory level, the book leads rapidly to important and often new results in synthetic differential geometry. From rudimentary analysis the book moves to such important results as: a new proof of De Rham's theorem; the synthetic view of global action, going as far as the Weil characteristic homomorphism; the systematic account of structured Lie objects, such as Riemannian, symplectic, or Poisson Lie objects; the view of global Lie algebras as Lie algebras of a Lie group in the synthetic sense; and lastly the synthetic construction of symplectic structure on the cotangent bundle in general. Thus while the book is limited to a naive point of view developing synthetic differential geometry as a theory in itself, the author nevertheless treats somewhat advanced topics, which are classic in classical differential geometry but new in the synthetic context. Audience: The book is suitable as an introduction to synthetic differential geometry for students as well as more qualified mathematicians.

Synthetic Differential Geometry

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Author : Anders Kock
Publisher : Cambridge University Press
ISBN 13 : 0521687381
Total Pages : 245 pages
Book Rating : 4.5/5 (216 download)

Book Synopsis Synthetic Differential Geometry by : Anders Kock

Download or read book Synthetic Differential Geometry written by Anders Kock and published by Cambridge University Press. This book was released on 2006-06-22 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2006, details how limit processes can be represented algebraically.

Synthetic Geometry of Manifolds

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Author : Anders Kock
Publisher : Cambridge University Press
ISBN 13 : 0521116732
Total Pages : 317 pages
Book Rating : 4.5/5 (211 download)

Book Synopsis Synthetic Geometry of Manifolds by : Anders Kock

Download or read book Synthetic Geometry of Manifolds written by Anders Kock and published by Cambridge University Press. This book was released on 2010 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This elegant book is sure to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighborhoods of the diagonal. These spaces enable a natural description of some of the basic constructions in local differential geometry and, in fact, form an inviting gateway to differential geometry, and also to some differential-geometric notions that exist in algebraic geometry. The presentation conveys the real strength of this approach to differential geometry. Concepts are clarified, proofs are streamlined, and the focus on infinitesimal spaces motivates the discussion well. Some of the specific differential-geometric theories dealt with are connection theory (notably affine connections), geometric distributions, differential forms, jet bundles, differentiable groupoids, differential operators, Riemannian metrics, and harmonic maps. Ideal for graduate students and researchers wishing to familiarize themselves with the field.

Differential Topology

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Author : J. Margalef-Roig
Publisher : Elsevier
ISBN 13 : 0080872840
Total Pages : 602 pages
Book Rating : 4.0/5 (88 download)

Book Synopsis Differential Topology by : J. Margalef-Roig

Download or read book Differential Topology written by J. Margalef-Roig and published by Elsevier. This book was released on 1992-06-02 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: ...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry. Peter W. Michor

Foundations of Differentiable Manifolds and Lie Groups

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Author : Frank W. Warner
Publisher : Springer Science & Business Media
ISBN 13 : 1475717997
Total Pages : 283 pages
Book Rating : 4.4/5 (757 download)

Book Synopsis Foundations of Differentiable Manifolds and Lie Groups by : Frank W. Warner

Download or read book Foundations of Differentiable Manifolds and Lie Groups written by Frank W. Warner and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds. The book also provides a proof of the de Rham theorem via sheaf cohomology theory and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem.

Real Analysis: A Comprehensive Course in Analysis, Part 1

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Author : Barry Simon
Publisher : American Mathematical Soc.
ISBN 13 : 1470410990
Total Pages : 789 pages
Book Rating : 4.4/5 (74 download)

Book Synopsis Real Analysis: A Comprehensive Course in Analysis, Part 1 by : Barry Simon

Download or read book Real Analysis: A Comprehensive Course in Analysis, Part 1 written by Barry Simon and published by American Mathematical Soc.. This book was released on 2015-11-02 with total page 789 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Fréchet spaces, Schwartz space, and spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.

Differential Topology and Quantum Field Theory

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Author : Charles Nash
Publisher : Elsevier
ISBN 13 : 9780125140768
Total Pages : 404 pages
Book Rating : 4.1/5 (47 download)

Book Synopsis Differential Topology and Quantum Field Theory by : Charles Nash

Download or read book Differential Topology and Quantum Field Theory written by Charles Nash and published by Elsevier. This book was released on 1991 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The remarkable developments in differential topology and how these recent advances have been applied as a primary research tool in quantum field theory are presented here in a style reflecting the genuinely two-sided interaction between mathematical physics and applied mathematics. The author, following his previous work (Nash/Sen: Differential Topology for Physicists, Academic Press, 1983), covers elliptic differential and pseudo-differential operators, Atiyah-Singer index theory, topological quantum field theory, string theory, and knot theory. The explanatory approach serves to illuminate and clarify these theories for graduate students and research workers entering the field for the first time. Treats differential geometry, differential topology, and quantum field theory Includes elliptic differential and pseudo-differential operators, Atiyah-Singer index theory, topological quantum field theory, string theory, and knot theory Tackles problems of quantum field theory using differential topology as a tool

Models for Smooth Infinitesimal Analysis

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Author : Ieke Moerdijk
Publisher : Springer Science & Business Media
ISBN 13 : 147574143X
Total Pages : 401 pages
Book Rating : 4.4/5 (757 download)

Book Synopsis Models for Smooth Infinitesimal Analysis by : Ieke Moerdijk

Download or read book Models for Smooth Infinitesimal Analysis written by Ieke Moerdijk and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to construct categories of spaces which contain all the C?-manifolds, but in addition infinitesimal spaces and arbitrary function spaces. To this end, the techniques of Grothendieck toposes (and the logic inherent to them) are explained at a leisurely pace and applied. By discussing topics such as integration, cohomology and vector bundles in the new context, the adequacy of these new spaces for analysis and geometry will be illustrated and the connection to the classical approach to C?-manifolds will be explained.

Differential Geometry and Topology

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Author : Keith Burns
Publisher : CRC Press
ISBN 13 : 1420057537
Total Pages : 403 pages
Book Rating : 4.4/5 (2 download)

Book Synopsis Differential Geometry and Topology by : Keith Burns

Download or read book Differential Geometry and Topology written by Keith Burns and published by CRC Press. This book was released on 2005-05-27 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. Smooth manifolds, Riemannian metrics

Differential Topology

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Author : David B. Gauld
Publisher : Courier Corporation
ISBN 13 : 0486319075
Total Pages : 256 pages
Book Rating : 4.4/5 (863 download)

Book Synopsis Differential Topology by : David B. Gauld

Download or read book Differential Topology written by David B. Gauld and published by Courier Corporation. This book was released on 2013-07-24 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text covers topological spaces and properties, some advanced calculus, differentiable manifolds, orientability, submanifolds and an embedding theorem, tangent spaces, vector fields and integral curves, Whitney's embedding theorem, more. Includes 88 helpful illustrations. 1982 edition.

The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics

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Author : John L. Bell
Publisher : Springer Nature
ISBN 13 : 3030187071
Total Pages : 313 pages
Book Rating : 4.0/5 (31 download)

Book Synopsis The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics by : John L. Bell

Download or read book The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics written by John L. Bell and published by Springer Nature. This book was released on 2019-09-09 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.

Elements of Differential Topology

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Author : Anant R. Shastri
Publisher : CRC Press
ISBN 13 : 1439831637
Total Pages : 319 pages
Book Rating : 4.4/5 (398 download)

Book Synopsis Elements of Differential Topology by : Anant R. Shastri

Download or read book Elements of Differential Topology written by Anant R. Shastri and published by CRC Press. This book was released on 2011-03-04 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Derived from the author's course on the subject, Elements of Differential Topology explores the vast and elegant theories in topology developed by Morse, Thom, Smale, Whitney, Milnor, and others. It begins with differential and integral calculus, leads you through the intricacies of manifold theory, and concludes with discussions on algebraic topol

New Foundations for Physical Geometry

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Author : Tim Maudlin
Publisher : Oxford University Press
ISBN 13 : 0198701306
Total Pages : 374 pages
Book Rating : 4.1/5 (987 download)

Book Synopsis New Foundations for Physical Geometry by : Tim Maudlin

Download or read book New Foundations for Physical Geometry written by Tim Maudlin and published by Oxford University Press. This book was released on 2014-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.

From Calculus to Cohomology

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Author : Ib H. Madsen
Publisher : Cambridge University Press
ISBN 13 : 9780521589567
Total Pages : 302 pages
Book Rating : 4.5/5 (895 download)

Book Synopsis From Calculus to Cohomology by : Ib H. Madsen

Download or read book From Calculus to Cohomology written by Ib H. Madsen and published by Cambridge University Press. This book was released on 1997-03-13 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory textbook on cohomology and curvature with emphasis on applications.

Differential Topology and Geometry with Applications to Physics

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Author : Eduardo Nahmad-Achar
Publisher : Institute of Physics Publishing
ISBN 13 : 9780750320733
Total Pages : 218 pages
Book Rating : 4.3/5 (27 download)

Book Synopsis Differential Topology and Geometry with Applications to Physics by : Eduardo Nahmad-Achar

Download or read book Differential Topology and Geometry with Applications to Physics written by Eduardo Nahmad-Achar and published by Institute of Physics Publishing. This book was released on 2018-12-21 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents, in a concise and direct manner, the appropriate mathematical formalism and fundamentals of differential topology and differential geometry, together with essential applications in many branches of physics.

Equivariant Topology and Derived Algebra

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Author : Scott Balchin
Publisher : Cambridge University Press
ISBN 13 : 1108931944
Total Pages : 357 pages
Book Rating : 4.1/5 (89 download)

Book Synopsis Equivariant Topology and Derived Algebra by : Scott Balchin

Download or read book Equivariant Topology and Derived Algebra written by Scott Balchin and published by Cambridge University Press. This book was released on 2021-11-18 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of research papers, both new and expository, based on the interests of Professor J. P. C. Greenlees.