Virtual Topology and Functor Geometry (Lecture Notes in Pure - download pdf or read online

By Fred Van Oystaeyen

ISBN-10: 1138430293

ISBN-13: 9781138430297

ISBN-10: 1420060562

ISBN-13: 9781420060560

Intrinsically noncommutative areas this day are thought of from the viewpoint of numerous branches of recent physics, together with quantum gravity, string thought, and statistical physics. From this standpoint, it's excellent to plan an idea of area and its geometry that's essentially noncommutative. supplying a transparent advent to noncommutative topology, digital Topology and Functor Geometry explores new elements of those components in addition to extra confirmed elements of noncommutative algebra.

Presenting the fabric in a simple, colloquial variety to facilitate knowing, the e-book starts off with an advent to classification concept, by way of a bankruptcy on noncommutative areas. This bankruptcy examines noncommutative lattices, noncommutative opens, sheaf concept, the generalized Stone area, and Grothendieck topology. the writer then reviews Grothendieck specific representations to formulate an summary thought of "affine open". the ultimate bankruptcy proposes a dynamical model of topology and sheaf conception, supplying no less than one resolution of the matter of sheafification self sufficient of generalizations of topos theory.

By proposing new rules for the improvement of an intrinsically noncommutative geometry, this ebook fosters the additional unification of other forms of noncommutative geometry and the expression of observations that contain traditional phenomena.

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