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Virtual Topology and Functor Geometry (Lecture Notes in Pure and Applied Mathematics) - Tapa blanda

Libro 38 de 138: Lecture Notes in Pure and Applied Mathematics

Oystaeyen, Fred Van

 
9781420060560: Virtual Topology and Functor Geometry (Lecture Notes in Pure and Applied Mathematics)
Tapa blanda
ISBN 10: 1420060562 ISBN 13: 9781420060560
Editorial: Chapman and Hall/CRC, 2007

Sinopsis

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 Geometry explores new aspects of these areas as well as more established facets of noncommutative algebra. Presenting the material in an easy, colloquial style to facilitate understanding, the book begins with an introduction to category theory, followed by a chapter on noncommutative spaces. This chapter examines noncommutative lattices, noncommutative opens, sheaf theory, the generalized Stone space, and Grothendieck topology. The author then studies Grothendieck categorical representations to formulate an abstract notion of "affine open". The final chapter proposes a dynamical version of topology and sheaf theory, providing at least one solution of the problem of sheafification independent of generalizations of topos theory. By presenting new ideas for the development of an intrinsically noncommutative geometry, this book fosters the further unification of different kinds of noncommutative geometry and the expression of observations that involve natural phenomena.

"Sinopsis" puede pertenecer a otra edición de este libro.

Acerca del autor

Fred Van Oystaeyen

De la contraportada

This work explores new aspects of virtual topology and functor geometry as well as more established facets of noncommutative algebra. The author suggests possible projects that range from straightforward exercises to advanced research level and supplies the necessary background material, including localization theory and the classical lattice of quantum mechanics for a Hilbert space. Presenting the material in an easy, colloquial style to facilitate understanding, he covers category theory and noncommutative spaces, formulates an abstract notion of "affine open" through Grothendieck categorical representations, and proposes a dynamical version of topology and sheaf theory.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Chapman and Hall/CRC
Año de publicación
2007
Idioma
Inglés
ISBN 10 
1420060562
ISBN 13 
9781420060560
Encuadernación
Tapa blanda
Número de edición
1
Número de páginas
168
Contacto del fabricante
Taylor and Francis, GPSR Taylor and Francis
gpsr@taylorandfrancis.com

Taylor & Francis Verlag GmbH, Kaufingerstraße 24
München
80331
Alemania