1601.06285Jan 23, 201645 pages. Update includes rationality results for spectra admitting a T-duality isomorphism, and extended comments on higher categorical aspects of iterated K-theory. Title changed from "A higher categorical analogue of topological T-duality for sphere bundles." To appear in Annals of K-theory
Twisted iterated algebraic K-theory and topological T-duality for sphere bundles
John A. Lind, Hisham Sati, Craig Westerland
Abstract
We introduce a periodic form of the iterated algebraic K-theory of ku, the (connective) complex K-theory spectrum, as well as a natural twisting of this cohomology theory by higher gerbes. Furthermore, we prove a form of topological T-duality for sphere bundles oriented with respect to this theory.