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Geometry of Principal Sheaves (Mathematics and Its Applications) - Efstathios Vassiliou
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Efstathios Vassiliou:
Geometry of Principal Sheaves (Mathematics and Its Applications) - pocketboek

ISBN: 9048168589

[SR: 16896195], Paperback, [EAN: 9789048168583], Springer, Springer, Book, [PU: Springer], Springer, The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities. Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is devoted to the theory of connections on principal sheaves, incorporating connections on vector and associated sheaves. Topics such as the moduli sheaf of connections, classification of principal sheaves, curvature, flat connections and flat sheaves, Chern-Weil theory, are also treated. The study brings to light fundamental notions and tools of the standard differential geometry which are susceptible of the present abstraction, and whose role remains unexploited in the classical context, because of the abundance of means therein. However, most of the latter are nonsensical in ADG., 13932, Differential Geometry, 226700, Geometry & Topology, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 13887, Algebra, 13889, Abstract, 13893, Elementary, 13897, Intermediate, 13899, Linear, 226698, Pure Mathematics, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 491542, Algebra & Trigonometry, 468218, Mathematics, 468216, Science & Mathematics, 465600, New, Used & Rental Textbooks, 2349030011, Specialty Boutique, 283155, Books, 491546, Geometry, 468218, Mathematics, 468216, Science & Mathematics, 465600, New, Used & Rental Textbooks, 2349030011, Specialty Boutique, 283155, Books

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Geometry of Principal Sheaves - Vassiliou, Efstathios
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Vassiliou, Efstathios:
Geometry of Principal Sheaves - pocketboek

2010, ISBN: 9789048168583

[ED: Softcover], [PU: Springer Netherlands], L inj enuit m eme d un regard neuf (celui de la science l est toujours) peut parfois clairer d un jour nouveau d anciens probl emes. J.Monod [77, p. 13] his book is intended as a comprehensive introduction to the theory of T principalsheaves andtheirconnections inthesettingofAbstractDi?- ential Geometry (ADG), the latter being initiated by A. Mallios sGeometry of Vector Sheaves [62]. Based on sheaf-theoretic methods and sheaf - homology, the presentGeometry of Principal Sheaves embodies the classical theory of connections on principal and vector bundles, and connections on vector sheaves, thus paving the way towards a uni?ed (abstract) gauge t- ory and other potential applications to theoretical physics. We elaborate on the aforementioned brief description in the sequel. Abstract (ADG) vs. Classical Di?erential Geometry (CDG). M- ern di?erential geometry is built upon the fundamental notions of di?er- tial (smooth) manifolds and ?ber bundles, based,intheir turn, on ordinary di?erential calculus. However, the theory of smooth manifolds is inadequate to cope, for - stance, with spaces like orbifolds, spaces with corners, or other spaces with more complicated singularities. This is a rather unfortunate situation, since one cannot apply the powerful methods of di?erential geometry to them or to any spaces that do not admit an ordinary method of di?erentiation. The ix x Preface same inadequacy manifests in physics, where many geometrical models of physical phenomena are non-smooth. Repr. 2005. 2010. xvi, 444 S. 240 mm Versandfertig in 3-5 Tagen, DE, [SC: 0.00], Neuware, gewerbliches Angebot, offene Rechnung (Vorkasse vorbehalten)

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Geometry of Principal Sheaves - Efstathios Vassiliou
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Efstathios Vassiliou:
Geometry of Principal Sheaves - gebruikt boek

ISBN: 9048168589

ID: 10860293

L' inj enuit m eme d' un regard neuf (celui de la science l'est toujours) peut parfois clairer d' un jour nouveau d' anciens probl emes. J.Monod 77, p. 13] his book is intended as a comprehensive introduction to the theory of T principalsheaves andtheirconnections inthesettingofAbstractDi?- ential Geometry (ADG), the latter being initiated by A. Mallios'sGeometry of Vector Sheaves 62]. Based on sheaf-theoretic methods and sheaf - homology, the presentGeometry of Principal Sheaves embodies the classical theory of connections on principal and vector bundles, and connections on vector sheaves, thus paving the way towards a uni'ed (abstract) gauge t- ory and other potential applications to theoretical physics. We elaborate on the aforementioned brief description in the sequel. Abstract (ADG) vs. Classical Di'erential Geometry (CDG). M- ern di'erential geometry is built upon the fundamental notions of di'er- tial (smooth) manifolds and ?ber bundles, based, intheir turn, on ordinary di'erential calculus. However, the theory of smooth manifolds is inadequate to cope, for - stance, with spaces like orbifolds, spaces with corners, or other spaces with more complicated singularities. This is a rather unfortunate situation, since one cannot apply the powerful methods of di'erential geometry to them or to any spaces that do not admit an ordinary method of di'erentiation. The ix x Preface same inadequacy manifests in physics, where many geometrical models of physical phenomena are non-smo math,mathematics,science and math Mathematics, Springer

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Geometry of Principal Sheaves - Efstathios Vassiliou
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Efstathios Vassiliou:
Geometry of Principal Sheaves - nieuw boek

ISBN: 9789048168583

ID: 978904816858

The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities.Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is devoted to the theory of connections on principal sheaves, incorporating connections on vector and associated sheaves. Topics such as the moduli sheaf of connections, classification of principal sheaves, curvature, flat connections and flat sheaves, Chern-Weil theory, are also treated. The study brings to light fundamental notions and tools of the standard differential geometry which are susceptible of the present abstraction, and whose role remains unexploited in the classical context, because of the abundance of means therein. However, most of the latter are nonsensical in ADG. Efstathios Vassiliou, Books, Science and Nature, Geometry of Principal Sheaves Books>Science and Nature, Springer Netherlands

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Geometry of Principal Sheaves - Vassiliou, Efstathios
uitverkocht boek
(*)
Vassiliou, Efstathios:
Geometry of Principal Sheaves - gebruikt boek

ISBN: 9789048168583

ID: 10988546

The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities. Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is devoted to the theory of connections on principal sheaves, incorporating connections on vector and associated sheaves. Topics such as the moduli sheaf of connections, classification of principal sheaves, curvature, flat connections and flat sheaves, Chern-Weil theory, are also treated. The study brings to light fundamental notions and tools of the standard differential geometry which are susceptible of the present abstraction, and whose role remains unexploited in the classical context, because of the abundance of means therein. However, most of the latter are nonsensical in ADG. Geometry of Principal Sheaves Vassiliou, Efstathios, Springer

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Bijzonderheden over het boek
Geometry of Principal Sheaves

The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities.Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is devoted to the theory of connections on principal sheaves, incorporating connections on vector and associated sheaves. Topics such as the moduli sheaf of connections, classification of principal sheaves, curvature, flat connections and flat sheaves, Chern-Weil theory, are also treated. The study brings to light fundamental notions and tools of the standard differential geometry which are susceptible of the present abstraction, and whose role remains unexploited in the classical context, because of the abundance of means therein. However, most of the latter are nonsensical in ADG.

Gedetalleerde informatie over het boek. - Geometry of Principal Sheaves


EAN (ISBN-13): 9789048168583
ISBN (ISBN-10): 9048168589
Gebonden uitgave
pocket book
Verschijningsjaar: 2011
Uitgever: Springer-Verlag GmbH
460 Bladzijden
Gewicht: 0,727 kg
Taal: eng/Englisch

Boek bevindt zich in het datenbestand sinds 12.07.2011 11:07:13
Boek voor het laatst gevonden op 16.04.2018 12:07:42
ISBN/EAN: 9789048168583

ISBN - alternatieve schrijfwijzen:
90-481-6858-9, 978-90-481-6858-3


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