Seminars: A. V. Ershov, Bundle gerbes and twisted K-theory (part I)

SEMINARS


Noncommutative geometry and topology October 30, 2014 16:45, Moscow, Lomonosov Moscow State Univ, Main Building, Faculty of Mechanics and Mathematics, auditorium 1604

Bundle gerbes and twisted K-theory (part I) A. V. Ershov
Abstract: In the talk I am going to outline the approach to the twisted K-theory taking bundle gerbes as twists. More precisely, we will construct a contravariant functor $X\rightarrow Tw(X)$ from spaces to (higher) groupoids. The objects of $Tw(X)$ are bundle gerbes $L$ over $X$, and 1-morphisms $L\rightarrow L'$ are a kind of $(L,L')$-bimodules. Although the Dixmier-Douady characteristic class determines a bijection between isomorphism classes of bundle gerbes over $X$ and the cohomology group $H^3(X,\mathbb{Z})$, the morphisms of $Tw(X)$ are equally important.