Geometry Of Principal Sheaves
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Geometry Of Principal Sheaves
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Author : Efstathios Vassiliou
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Geometry Of Principal Sheaves written by Efstathios Vassiliou 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 2006-03-30 with Mathematics categories.
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 Vector Sheaves
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Author : Anastasios Mallios
language : en
Publisher: Springer Science & Business Media
Release Date : 1998
Geometry Of Vector Sheaves written by Anastasios Mallios 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 1998 with Mathematics categories.
This is the second volume of a two-volume monograph which obtains fundamental notions and results of the standard differential geometry of smooth manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasized. This has theoretical advantages such as greater perspective, clarity and unification, but also practical benefits ranging from elementary particle physics, via gauge theories and theoretical cosmology (differential spaces), to non-linear PDEs (generalized functions). Thus, more general applications, which are no longer smooth in the classical sense, can be coped with. The treatise might also be construed as a new systematic endeavour to confront the ever-increasing notion that the world around us is far from being smooth enough.
The Geometry Of Moduli Spaces Of Sheaves
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Author : Daniel Huybrechts
language : en
Publisher: Cambridge University Press
Release Date : 2010-05-27
The Geometry Of Moduli Spaces Of Sheaves written by Daniel Huybrechts 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 2010-05-27 with Mathematics categories.
This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.
Modern Differential Geometry In Gauge Theories
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Author : Anastasios Mallios
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-27
Modern Differential Geometry In Gauge Theories written by Anastasios Mallios 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 2006-07-27 with Mathematics categories.
This is original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable
Flat Principal Sheaves
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Author : Efstathios Vassiliou
language : en
Publisher:
Release Date : 1997
Flat Principal Sheaves written by Efstathios Vassiliou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mechanics, Analytic categories.
New Developments In Differential Geometry Budapest 1996
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Author : J. Szenthe
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
New Developments In Differential Geometry Budapest 1996 written by J. Szenthe 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.
Proceedings of the Conference on Differential Geometry, Budapest, Hungary, July 27-30, 1996
Connections On Principal Sheaves
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Author : Efstathios Vassiliou
language : en
Publisher:
Release Date : 1997
Connections On Principal Sheaves written by Efstathios Vassiliou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mechanics, Analytic categories.
Sheaves In Geometry And Logic
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Author : Saunders MacLane
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-10-27
Sheaves In Geometry And Logic written by Saunders MacLane 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 1994-10-27 with Mathematics categories.
Sheaves arose in geometry as coefficients for cohomology and as descriptions of the functions appropriate to various kinds of manifolds. Sheaves also appear in logic as carriers for models of set theory. This text presents topos theory as it has developed from the study of sheaves. Beginning with several examples, it explains the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic.
Lectures On The Geometry Of Position
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Author : Theodor Reye
language : en
Publisher:
Release Date : 1898
Lectures On The Geometry Of Position written by Theodor Reye and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1898 with Geometry, Projective categories.
Principal Bundles
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Author : Stephen Bruce Sontz
language : en
Publisher: Springer
Release Date : 2015-04-20
Principal Bundles written by Stephen Bruce Sontz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-20 with Science categories.
This introductory text is the first book about quantum principal bundles and their quantum connections which are natural generalizations to non-commutative geometry of principal bundles and their connections in differential geometry. To make for a more self-contained book there is also much background material on Hopf algebras, (covariant) differential calculi, braid groups and compatible conjugation operations. The approach is slow paced and intuitive in order to provide researchers and students in both mathematics and physics ready access to the material.