4 may 2016 -- 14:30
Aula di Consiglio, Dip.Matematica, Università "La Sapienza", Roma
Abstract.
Twists for various cohomology theories play an important role in various areas of mathematics as well as in mathematical physics. I will survey this area, starting with twisted de Rham cohomology, twisted K-theory, and then considering higher twists from the point of view of generalized cohomology theories of higher chromatic and categorical levels. I will describe joint work with Craig Westerland on twists of Morava K-theory and E-theory, descending from complex cobordism, at all chromatic levels. Then I will describe recent work with John Lind and Craig Westerland on a new periodic form of the iterated algebraic K-theory of connective complex K-theory ku, generalizing the K-theory of 2-vector bundles K(ku) to all categorical degrees, as well as a natural twisting of this cohomology theory by higher gerbes. As an application, this leads to topological T-duality for sphere bundles oriented with respect to this theory as an isomorphism of the twisted theories, generalizing various existing results.