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This two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth (CINFINITY) manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasised. 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 (generalised 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'. Audience: 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.
| Autorius: | Anastasios Mallios |
| Serija: | Mathematics and Its Applications |
| Leidėjas: | Springer Netherlands |
| Išleidimo metai: | 1998 |
| Knygos puslapių skaičius: | 936 |
| ISBN-10: | 0792350065 |
| ISBN-13: | 9780792350064 |
| Formatas: | 241 x 160 x 62 mm. Knyga kietu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications“
