Twisted K theory

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, twisted K-theory (also called "K-theory with local coefficients") is a variation on K-theory, a mathematical theory from the 1950s that spans algebraic topology, abstract algebra and operator theory.More specifically, twisted K-theory with twist H is a particular variant of K-theory, in which the twist is given by an integral 3-dimensional cohomology class. It is special among the various twists that K-theory admits for two reasons. First, it admits a geometric formulation. This was provided in two steps ; the first one was done in 1970 (Publ. Math. de l'IHES) by Peter Donovan and Max Karoubi ; the second one in 1988 by Jonathan Rosenberg in Continuous-Trace Algebras from the Bundle Theoretic Point of View.