Year: 2026
Type: article
Abstract: We compute the first two k-invariants of the Picard spectra of KU and KO by analyzing their Picard groupoids and constructing their unit spectra as global sections of sheaves on the category of manifolds.This allows us to determine the E 1 -structures of their truncations Pic.KU/Œ0; 3 and Pic.KO/Œ0; 2. It follows that these truncated Picard spaces represent the Brauer groups of Z=2-graded algebra bundles of Donovan, Karoubi, Moutuou and Maycock; the Brauer groups of super 2-lines; and the K-theory twists of Freed, Hopkins and Teleman.Our results also imply that these spaces represent twists of Stringand Spin-structures on manifolds and can be used to twist tmf-cohomology.Finally, we are able to identify pic.KU/Œ0; 3 with a cotruncation of the Anderson dual of the sphere spectrum.
Source: Algebraic & Geometric Topology
Authors: Jonathan Beardsley, Kiran Luecke, Jack Morava
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4381587493