Geometry of principal sheaves
Author:
Series:
Mathematics and its applications volume 578
Publisher:
Springer
Pub. Date:
©2005
Language:
English
Description
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.
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Contributors:
ISBN:
9781402034152
9781402034169
9786610283880
9781280283888
9781402034169
9786610283880
9781280283888
Staff View
Grouping Information
Grouped Work ID | 7d461a29-0ab6-11ad-e5bb-ee02658a2ce9 |
---|---|
Grouping Title | geometry of principal sheaves |
Grouping Author | e vassiliou |
Grouping Category | book |
Grouping Language | English (eng) |
Last Grouping Update | 2024-05-01 10:09:19AM |
Last Indexed | 2024-05-05 00:11:25AM |
Solr Fields
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author
Vassiliou, E. (Efstathios)
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SpringerLink (Online Service)
author_display
Vassiliou, E.
available_at_ccu
CCU Electronic Resources
detailed_location_ccu
CCU Electronic Resources
display_description
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.
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eBook
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eBook
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7d461a29-0ab6-11ad-e5bb-ee02658a2ce9
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9781280283888
9781402034152
9781402034169
9786610283880
9781402034152
9781402034169
9786610283880
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E-book
last_indexed
2024-05-05T06:11:25.160Z
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Non Fiction
literary_form_full
Non Fiction
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Colorado Christian University Online
owning_location_ccu
CCU Electronic Resources
primary_isbn
9781402034152
publishDate
2005
publisher
Springer
recordtype
grouped_work
series
Mathematics and its applications
series_with_volume
Mathematics and its applications|578
subject_facet
Geometry, Differential
Geometría diferencial
Géométrie différentielle
MATHEMATICS -- Geometry -- Differential
Geometría diferencial
Géométrie différentielle
MATHEMATICS -- Geometry -- Differential
title_display
Geometry of principal sheaves
title_full
Geometry of principal sheaves / by Efstathios Vassiliou
title_short
Geometry of principal sheaves
topic_facet
Differential
Geometry
Geometry, Differential
Geometría diferencial
Géométrie différentielle
MATHEMATICS
Geometry
Geometry, Differential
Geometría diferencial
Géométrie différentielle
MATHEMATICS
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