Year: 2026
Type: preprint
Abstract: We study projective and semidirect quotients of the spherical Milnor construction and develop a step-by-step lifting obstruction from their explicit spherical local sections. The resulting transition functions produce a twisted Cech 2-cocycle for any specified compatible extension with abelian kernel. When the kernel is $U(1)$ and the sign acts by complex conjugation, taking logarithms yields a twisted Dixmier--Douady obstruction under stated sheaf hypotheses. We identify its projective-operator interpretation when an additional representation is supplied, without attempting a classification of K-theory twists. We also investigate descent of differential-geometric structures and, under restricted-operator hypotheses, Schwinger cocycles and lifting gerbes for loop groups.
Source: arXiv (Cornell University)
Author: Magnot, Jean-Pierre
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161698226