Spherical Milnor Spaces II: Projective Quotients and Higher Topological Structures
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.
Related
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BibTeX
@misc{magnot2026spherical,
title = {{Spherical Milnor Spaces II: Projective Quotients and Higher Topological Structures}},
author = {Jean-Pierre Magnot},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.16370},
eprint = {2605.16370},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.16370},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spherical Milnor Spaces II: Projective Quotients and Higher Topological Structures
AU - Jean-Pierre Magnot
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2605.16370
UR - https://arxiv.org/abs/2605.16370
AB - 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.
ER -