168 Pages
51 B/W Illustrations
by
Chapman & Hall
168 Pages
by
Chapman & Hall
168 Pages
by
Chapman & Hall
Also available as eBook on:
Intrinsically noncommutative spaces today are considered from the perspective of several branches of modern physics, including quantum gravity, string theory, and statistical physics. From this point of view, it is ideal to devise a concept of space and its geometry that is fundamentally noncommutative. Providing a clear introduction to noncommutative topology, Virtual Topology and Functor... Read more
FOREWORD
INTRODUCTION
PROJECTS
A TASTE OF CATEGORY THEORY
Basic Notions
Grothendieck Categories
Separable Functors
NONCOMMUTATIVE SPACES
Small Categories, Posets, and Noncommutative Topologies
The Topology of Virtual Opens and Its Commutative Shadow
Points and the Point Spectrum: Points in a Pointless World
Presheaves and Sheaves over Noncommutative Topologies
Noncommutative Grothendieck Topologies
The Fundamental Examples I: Torsion Theories
The Fundamental Examples II: L(H)
Ore Sets in Schematic Algebras
GROTHENDIECK CATEGORICAL REPRESENTATIONS
Spectral Representations
Affine Elements
Quotient Representations
Noncommutative Projective Space
SHEAVES AND DYNAMICAL TOPOLOGY
Introducing Structure Sheaves
Dynamical Presheaves and Temporal Points
The Spaced-Time Model
BIBLIOGRAPHY
INDEX
INTRODUCTION
PROJECTS
A TASTE OF CATEGORY THEORY
Basic Notions
Grothendieck Categories
Separable Functors
NONCOMMUTATIVE SPACES
Small Categories, Posets, and Noncommutative Topologies
The Topology of Virtual Opens and Its Commutative Shadow
Points and the Point Spectrum: Points in a Pointless World
Presheaves and Sheaves over Noncommutative Topologies
Noncommutative Grothendieck Topologies
The Fundamental Examples I: Torsion Theories
The Fundamental Examples II: L(H)
Ore Sets in Schematic Algebras
GROTHENDIECK CATEGORICAL REPRESENTATIONS
Spectral Representations
Affine Elements
Quotient Representations
Noncommutative Projective Space
SHEAVES AND DYNAMICAL TOPOLOGY
Introducing Structure Sheaves
Dynamical Presheaves and Temporal Points
The Spaced-Time Model
BIBLIOGRAPHY
INDEX
Biography
Fred Van Oystaeyen
"This book has a special character. Its main theme is to describe development of new branches of non-commutative geometry on a different level of realizations, ranging from areas already fully developed to many different suggestions for possible future investigations. … the book is very inspiring and worth reading."
—EMS Newsletter, December 2009
