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.
| ISBN: | 9780792350064 |
| Publication date: | 30th April 1998 |
| Author: | Anastasios Mallios |
| Publisher: | Springer an imprint of Springer Netherlands |
| Format: | Hardback |
| Series: | Mathematics and Its Applications |
| Genres: |
Differential and Riemannian geometry Algebraic topology Complex analysis, complex variables Functional analysis and transforms Calculus and mathematical analysis |