Synthetic Differential Geometry
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Basic Concepts Of Synthetic Differential Geometry
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Author : R. Lavendhomme
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Basic Concepts Of Synthetic Differential Geometry written by R. Lavendhomme 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 2013-03-09 with Mathematics categories.
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
language : en
Publisher: Cambridge University Press
Release Date : 2006-06-22
Synthetic Differential Geometry written by Anders Kock 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 2006-06-22 with Mathematics categories.
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
language : en
Publisher: Cambridge University Press
Release Date : 2010
Synthetic Geometry Of Manifolds written by Anders Kock 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 with Mathematics categories.
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.
Recent Synthetic Differential Geometry
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Author : Herbert Busemann
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Recent Synthetic Differential Geometry written by Herbert Busemann 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.
A synthetic approach to intrinsic differential geometry in the large and its connections with the foundations of geometry was presented in "The Geometry of Geodesics" (1955, quoted as G). It is the purpose of the present report to bring this theory up to date. Many of the later ip.vestigations were stimulated by problems posed in G, others concern newtopics. Naturally references to G are frequent. However, large parts, in particular Chapters I and III as weIl as several individual seetions, use only the basic definitions. These are repeated here, sometimes in a slightly different form, so as to apply to more general situations. In many cases a quoted result is quite familiar in Riemannian Geometry and consulting G will not be found necessary. There are two exceptions : The theory of paralleIs is used in Sections 13, 15 and 17 without reformulating all definitions and properties (of co-rays and limit spheres). Secondly, many items from the literature in G (pp. 409-412) are used here and it seemed superfluous to include them in the present list of references (pp. 106-110). The quotations are distinguished by [ ] and ( ), so that, for example, FreudenthaI [1] and (I) are found, respectively, in G and here.
Synthetic Differential Topology
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Author : Marta Bunge
language : en
Publisher: Cambridge University Press
Release Date : 2018-03-29
Synthetic Differential Topology written by Marta Bunge 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 2018-03-29 with Mathematics categories.
Represents the state of the art in the new field of synthetic differential topology.
Synthetic Differential Geometry Models
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Author : Anders Kock
language : en
Publisher:
Release Date : 2006
Synthetic Differential Geometry Models written by Anders Kock and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Geometry, Differential categories.
Second edition of this book detailing how limit processes can be represented algebraically.
Synthetic Differential Topology
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Author : Marta Bunge
language : en
Publisher:
Release Date : 2018
Synthetic Differential Topology written by Marta Bunge and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with MATHEMATICS categories.
Represents the state of the art in the new field of synthetic differential topology.
Models For Smooth Infinitesimal Analysis
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Author : Ieke Moerdijk
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Models For Smooth Infinitesimal Analysis written by Ieke Moerdijk 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 2013-03-14 with Mathematics categories.
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.
A Primer Of Infinitesimal Analysis
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Author : John L. Bell
language : en
Publisher: Cambridge University Press
Release Date : 2008-04-07
A Primer Of Infinitesimal Analysis written by John L. Bell 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 2008-04-07 with Mathematics categories.
A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.
The Ambrose Palais Singer Theorem In Synthetic Differential Geometry Microform
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Author : Michel Nystrom
language : en
Publisher: National Library of Canada
Release Date : 1987
The Ambrose Palais Singer Theorem In Synthetic Differential Geometry Microform written by Michel Nystrom and has been published by National Library of Canada this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Connections (Mathematics) categories.