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Geometry of Principal Sheavesby Efstathios Vassiliou
Springer 2005; US$ 149.00The 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,... more...
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Cambridge University Press 1975; US$ 53.00Sheaf theory provides a means of discussing many different kinds of geometric objects in respect of the connection between their local and global properties. more...
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