Geometry Of Principal Sheaves

Author : Efstathios Vassiliou
Publisher : Springer Science & Business Media
ISBN 13 : 1402034164
Total Pages : 454 pages
Book Rating : 4.69/5 ( download)

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Download or read book Geometry of Principal Sheaves written by Efstathios Vassiliou and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Daniel Huybrechts
Publisher : Cambridge University Press
ISBN 13 : 1139485822
Total Pages : 345 pages
Book Rating : 4.21/5 ( download)

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Download or read book The Geometry of Moduli Spaces of Sheaves written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2010-05-27 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Anastasios Mallios
Publisher : Springer Science & Business Media
ISBN 13 : 0817646345
Total Pages : 244 pages
Book Rating : 4.49/5 ( download)

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Download or read book Modern Differential Geometry in Gauge Theories written by Anastasios Mallios and published by Springer Science & Business Media. This book was released on 2009-10-22 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Anastasios Mallios
Publisher : Springer Science & Business Media
ISBN 13 : 9780792350057
Total Pages : 468 pages
Book Rating : 4.57/5 ( download)

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Download or read book Geometry of Vector Sheaves written by Anastasios Mallios and published by Springer Science & Business Media. This book was released on 1998 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Efstathios Vassiliou
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.73/5 ( download)

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Download or read book Connections on Principal Sheaves written by Efstathios Vassiliou and published by . This book was released on 1997 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Piotr Pragacz
Publisher : Springer Science & Business Media
ISBN 13 : 3764385375
Total Pages : 240 pages
Book Rating : 4.78/5 ( download)

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Download or read book Algebraic Cycles, Sheaves, Shtukas, and Moduli written by Piotr Pragacz and published by Springer Science & Business Media. This book was released on 2008-03-12 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles examine the contributions of the great mathematician J. M. Hoene-Wronski. Although much of his work was dismissed during his lifetime, it is now recognized that his work offers valuable insight into the nature of mathematics. The book begins with elementary-level discussions and ends with discussions of current research. Most of the material has never been published before, offering fresh perspectives on Hoene-Wronski’s contributions.

Author : J. Szenthe
Publisher : Springer Science & Business Media
ISBN 13 : 9401152764
Total Pages : 513 pages
Book Rating : 4.61/5 ( download)

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Download or read book New Developments in Differential Geometry, Budapest 1996 written by J. Szenthe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Conference on Differential Geometry, Budapest, Hungary, July 27-30, 1996

Author : Efstathios Vassiliou
Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.74/5 ( download)

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Download or read book Flat Principal Sheaves written by Efstathios Vassiliou and published by . This book was released on 1997 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Efstathios Vassiliou
Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.60/5 ( download)

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Download or read book Flat Principal Sheaves written by Efstathios Vassiliou and published by . This book was released on 1997 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Patrick Cabau
Publisher : CRC Press
ISBN 13 : 1000966011
Total Pages : 1516 pages
Book Rating : 4.15/5 ( download)

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Download or read book Direct and Projective Limits of Geometric Banach Structures. written by Patrick Cabau and published by CRC Press. This book was released on 2023-10-06 with total page 1516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes in detail the basic context of the Banach setting and the most important Lie structures found in finite dimension. The authors expose these concepts in the convenient framework which is a common context for projective and direct limits of Banach structures. The book presents sufficient conditions under which these structures exist by passing to such limits. In fact, such limits appear naturally in many mathematical and physical domains. Many examples in various fields illustrate the different concepts introduced. Many geometric structures, existing in the Banach setting, are "stable" by passing to projective and direct limits with adequate conditions. The convenient framework is used as a common context for such types of limits. The contents of this book can be considered as an introduction to differential geometry in infinite dimension but also a way for new research topics. This book allows the intended audience to understand the extension to the Banach framework of various topics in finite dimensional differential geometry and, moreover, the properties preserved by passing to projective and direct limits of such structures as a tool in different fields of research.