Geometry of Principal Sheaves [electronic resource] /
Vassiliou, Efstathios.author.
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
Description based upon print version of record.
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
Includes bibliographical references and index.
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.
Differential geometry.
Differential Geometry.
Mathematics and its applications