Twisted iterated algebraic K-theory and topological T-duality for sphere bundles

John A. Lind, Hisham Sati, Craig Westerland

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)1-42
Number of pages42
JournalAnnals of K-Theory
Volume5
Issue number1
DOIs
StatePublished - 2020

Bibliographical note

Funding 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 [1983]. 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.

Publisher Copyright:
© 2020 Mathematical Sciences Publishers.

Keywords

  • Iterated algebraic K-theory
  • N-gerbes
  • T-duality
  • Twisted K-theory

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