Virtual Topology and Functor Geometry (Lecture Notes in Pure by Fred Van Oystaeyen

By Fred Van Oystaeyen

Intrinsically noncommutative areas at the present time are thought of from the point of view of numerous branches of contemporary physics, together with quantum gravity, string thought, and statistical physics. From this standpoint, it's perfect to plan an idea of house and its geometry that's essentially noncommutative. offering a transparent creation to noncommutative topology, digital Topology and Functor Geometry explores new features of those components in addition to extra demonstrated points of noncommutative algebra.

Presenting the fabric in a simple, colloquial sort to facilitate realizing, the e-book starts with an creation to classification conception, through a bankruptcy on noncommutative areas. This bankruptcy examines noncommutative lattices, noncommutative opens, sheaf conception, the generalized Stone area, and Grothendieck topology. the writer then stories Grothendieck specific representations to formulate an summary proposal of "affine open". the ultimate bankruptcy proposes a dynamical model of topology and sheaf thought, offering at the least one answer of the matter of sheafification self sustaining of generalizations of topos theory.

By featuring new rules for the advance of an intrinsically noncommutative geometry, this ebook fosters the additional unification of alternative types of noncommutative geometry and the expression of observations that contain ordinary phenomena.

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