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In today's research, intrinsically noncommutative spaces 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 seems necessary to have a concept of space and its geometry that is fundamentally noncommutative. Virtual Topology and Functor Geometry presents new ideas for the development of an intrinsically noncommutative geometry. Written in an easily accessible, colloquial style, the book provides numerous suggestions for possible projects, ranging from exercise level to research…mehr

Produktbeschreibung
In today's research, intrinsically noncommutative spaces 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 seems necessary to have a concept of space and its geometry that is fundamentally noncommutative. Virtual Topology and Functor Geometry presents new ideas for the development of an intrinsically noncommutative geometry. Written in an easily accessible, colloquial style, the book provides numerous suggestions for possible projects, ranging from exercise level to research level. Topics covered include Grothendieck categorical representations and structure sheaves.
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.
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Autorenporträt
Fred Van Oystaeyen