The Resource Geometry of principal sheaves, by Efstathios Vassiliou
Geometry of principal sheaves, by Efstathios Vassiliou
Resource Information
The item Geometry of principal sheaves, by Efstathios Vassiliou represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Geometry of principal sheaves, by Efstathios Vassiliou represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 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 nonsmooth 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, ChernWeil 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
 Language
 eng
 Extent
 1 online resource (xvi, 444 pages)
 Contents

 Sheaves and all that
 The category of differential triads
 Lie sheaves of groups
 Principal sheaves
 Vector and associated sheaves
 Connections on principal sheaves
 Connections on vector and associated sheaves
 Curvature
 ChernWeil theory
 Applications and further examples
 Bibliography
 List of symbols
 Subject index
 Isbn
 9781402034169
 Label
 Geometry of principal sheaves
 Title
 Geometry of principal sheaves
 Statement of responsibility
 by Efstathios Vassiliou
 Language
 eng
 Summary
 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 nonsmooth 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, ChernWeil 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
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorName
 Vassiliou, E.
 Dewey number
 516.36
 Illustrations
 illustrations
 Index
 index present
 Language note
 English
 LC call number
 QA612.36
 LC item number
 .V37 2005eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Mathematics and its applications Dordrecht
 Series volume
 vol. 578
 http://library.link/vocab/subjectName

 Geometry, Differential
 MATHEMATICS
 Geometry, Differential
 Label
 Geometry of principal sheaves, by Efstathios Vassiliou
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Sheaves and all that  The category of differential triads  Lie sheaves of groups  Principal sheaves  Vector and associated sheaves  Connections on principal sheaves  Connections on vector and associated sheaves  Curvature  ChernWeil theory  Applications and further examples  Bibliography  List of symbols  Subject index
 Control code
 209846102
 Dimensions
 unknown
 Extent
 1 online resource (xvi, 444 pages)
 Form of item
 online
 Isbn
 9781402034169
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/1402034164
 Other physical details
 illustrations.
 http://library.link/vocab/ext/overdrive/overdriveId
 9781402034152
 Specific material designation
 remote
 System control number
 (OCoLC)209846102
 Label
 Geometry of principal sheaves, by Efstathios Vassiliou
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Sheaves and all that  The category of differential triads  Lie sheaves of groups  Principal sheaves  Vector and associated sheaves  Connections on principal sheaves  Connections on vector and associated sheaves  Curvature  ChernWeil theory  Applications and further examples  Bibliography  List of symbols  Subject index
 Control code
 209846102
 Dimensions
 unknown
 Extent
 1 online resource (xvi, 444 pages)
 Form of item
 online
 Isbn
 9781402034169
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/1402034164
 Other physical details
 illustrations.
 http://library.link/vocab/ext/overdrive/overdriveId
 9781402034152
 Specific material designation
 remote
 System control number
 (OCoLC)209846102
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/GeometryofprincipalsheavesbyEfstathios/azyl0M2NOIY/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/GeometryofprincipalsheavesbyEfstathios/azyl0M2NOIY/">Geometry of principal sheaves, by Efstathios Vassiliou</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>