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.
Bibliographical noteFunding Information:
We thank Ben Antieau, Justin Noel, and Thomas Schick for helpful comments on a previous draft and Drew Heard for pointing us to the paper of Arthan . We also thank Rune Haugseng for sharing his perspectives on higher category theory and iterated K -theory with us. Lind was supported in part by the DFG through SFB1085. Sati thanks the Erwin Schrödinger Institute for Mathematical Physics, Vienna, for hospitality and the organizers of the program “Higher Structures in String Theory” for the opportunity to present the results of this project. Westerland was supported in part by the NSF through DMS-1406162.
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- Iterated algebraic K-theory
- Twisted K-theory