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Geometry - Examples and Applications (v. 2): An Axiomatic Approach to Differential Geometry, 2 (Mathematics and its Applications) - Hardcover
Synopsis
This is the second volume of a two-volume monograph which obtains fundamental notions and results of the standard differential geometry of smooth manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasized. This has theoretical advantages such as greater perspective, clarity and unification, but also practical benefits ranging from elementary particle physics, via gauge theories and theoretical cosmology ("differential spaces"), to non-linear PDEs (generalized functions). Thus, more general applications, which are no longer "smooth" in the classical sense, can be coped with. The treatise might also be construed as a new systematic endeavour to confront the ever-increasing notion that the "world around us is far from being smooth enough". This work is intended for postgraduate students and researchers whose work involves differential geometry, global analysis, analysis on manifolds, algebraic topology, sheaf theory, cohomology, functional analysis or abstract harmonic analysis.
"synopsis" may belong to another edition of this title.
- PublisherKluwer Academic Publishers
- Publication date1998
- ISBN 10 0792350057
- ISBN 13 9780792350057
- BindingHardcover
- LanguageEnglish
- Number of pages462
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