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 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
- 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
- Chern-Weil 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 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
- 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 -- Chern-Weil 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
- 10.1007/1-4020-3416-4
- Other physical details
- illustrations.
- http://library.link/vocab/ext/overdrive/overdriveId
- 978-1-4020-3415-2
- 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 -- Chern-Weil 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
- 10.1007/1-4020-3416-4
- Other physical details
- illustrations.
- http://library.link/vocab/ext/overdrive/overdriveId
- 978-1-4020-3415-2
- Specific material designation
- remote
- System control number
- (OCoLC)209846102
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Geometry-of-principal-sheaves-by-Efstathios/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/Geometry-of-principal-sheaves-by-Efstathios/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>
