Geometry of Vector Sheaves : an Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications /
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 un...
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| Format: | eBook |
| Language: | English |
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Dordrecht :
Springer Netherlands : Imprint : Springer,
1998.
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| Series: | Mathematics and Its Applications ;
439. |
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (XXIII, 438 pages) |
| ISBN: | 9789401150064 (electronic bk.) 9401150060 (electronic bk.) |