Geometry of Vector Sheaves
Title | Geometry of Vector Sheaves PDF eBook |
Author | Anastasios Mallios |
Publisher | Springer Science & Business Media |
Pages | 468 |
Release | 1998 |
Genre | Mathematics |
ISBN | 9780792350040 |
This text is part 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.
Geometry of Vector Sheaves: Vector sheaves. General theory
Title | Geometry of Vector Sheaves: Vector sheaves. General theory PDF eBook |
Author | Anastasios Mallios |
Publisher | |
Pages | |
Release | 1998 |
Genre | Geometry, Differential |
ISBN |
Geometry of Vector Sheaves
Title | Geometry of Vector Sheaves PDF eBook |
Author | Anastasios Mallios |
Publisher | Springer Science & Business Media |
Pages | 457 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 9401150060 |
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.
Modern Differential Geometry in Gauge Theories
Title | Modern Differential Geometry in Gauge Theories PDF eBook |
Author | Anastasios Mallios |
Publisher | Springer Science & Business Media |
Pages | 303 |
Release | 2006-07-27 |
Genre | Mathematics |
ISBN | 0817644741 |
This is original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable
Modern Differential Geometry in Gauge Theories
Title | Modern Differential Geometry in Gauge Theories PDF eBook |
Author | Anastasios Mallios |
Publisher | Springer Science & Business Media |
Pages | 244 |
Release | 2009-10-22 |
Genre | Mathematics |
ISBN | 0817646345 |
Original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable
Vector sheaves. General theory. Mallios
Title | Vector sheaves. General theory. Mallios PDF eBook |
Author | |
Publisher | |
Pages | |
Release | |
Genre | |
ISBN |
Modern Differential Geometry in Gauge Theories
Title | Modern Differential Geometry in Gauge Theories PDF eBook |
Author | Anastasios Mallios |
Publisher | Birkhäuser |
Pages | 293 |
Release | 2008-11-01 |
Genre | Mathematics |
ISBN | 9780817670900 |
This is original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable