Geometry of Vector Sheaves: Geometry. Examples and applications
Title | Geometry of Vector Sheaves: Geometry. Examples and applications 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.
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 | 9780792350057 |
This is the second volume 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 Principal Sheaves
Title | Geometry of Principal Sheaves PDF eBook |
Author | Efstathios Vassiliou |
Publisher | Springer Science & Business Media |
Pages | 454 |
Release | 2006-03-30 |
Genre | Mathematics |
ISBN | 1402034164 |
The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities. Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is devoted to the theory of connections on principal sheaves, incorporating connections on vector and associated sheaves. Topics such as the moduli sheaf of connections, classification of principal sheaves, curvature, flat connections and flat sheaves, Chern-Weil theory, are also treated. The study brings to light fundamental notions and tools of the standard differential geometry which are susceptible of the present abstraction, and whose role remains unexploited in the classical context, because of the abundance of means therein. However, most of the latter are nonsensical in ADG.
Vector Geometry
Title | Vector Geometry PDF eBook |
Author | Gilbert de B. Robinson |
Publisher | Courier Corporation |
Pages | 194 |
Release | 2013-10-10 |
Genre | Mathematics |
ISBN | 0486321045 |
Concise undergraduate-level text by a prominent mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement. Includes answers to exercises. 1962 edition.
The Geometry of Moduli Spaces of Sheaves
Title | The Geometry of Moduli Spaces of Sheaves PDF eBook |
Author | Daniel Huybrechts |
Publisher | Cambridge University Press |
Pages | 345 |
Release | 2010-05-27 |
Genre | Mathematics |
ISBN | 1139485822 |
This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.
Algebraic Geometry 2
Title | Algebraic Geometry 2 PDF eBook |
Author | Kenji Ueno |
Publisher | American Mathematical Soc. |
Pages | 196 |
Release | 1999 |
Genre | Mathematics |
ISBN | 9780821813577 |
Algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes was explained in Algebraic Geometry 1: From Algebraic Varieties to Schemes. In this volume, the author turns to the theory of sheaves and their cohomology. A sheaf is a way of keeping track of local information defined on a topological space, such as the local holomorphic functions on a complex manifold or the local sections of a vector bundle. To study schemes, it is useful to study the sheaves defined on them, especially the coherent and quasicoherent sheaves.