Geometry of Torsion Gerbes and Flat Twisted Vector Bundles

Autor:	Byungdo Park
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	gerbe 2-gerbe smooth Deligne cohomology Dixmier–Douady class twisted vector bundles Mathematics QA1-939
Zdroj:	Axioms, Vol 13, Iss 8, p 504 (2024)
Druh dokumentu:	article
ISSN:	13080504 2075-1680
DOI:	10.3390/axioms13080504
Popis:	Gerbes and higher gerbes are geometric cocycles representing higher degree cohomology classes, and are attracting considerable interest in differential geometry and mathematical physics. We prove that a 2-gerbe has a torsion Dixmier–Douady class if and only if the gerbe has locally constant cocycle data. As an application, we give an alternative description of flat twisted vector bundles in terms of locally constant transition maps. These results generalize to n-gerbes for n=1 and n≥3, providing insights into the structure of higher gerbes and their applications to the geometry of twisted vector bundles.
Databáze:	Directory of Open Access Journals
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