Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications - Couverture rigide

Mallios, Anastasios

 
9780792350064: Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Autres éditions populaires du même titre

9780792350057: Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry, 2

Edition présentée

ISBN 10 :  0792350057 ISBN 13 :  9780792350057
Editeur : Kluwer Academic Publishers, 1998
Couverture rigide