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The fundamental Gray 3-groupoid of a smooth manifold and local 3-dimensional holonomy based on a 2-crossed module

TítuloThe fundamental Gray 3-groupoid of a smooth manifold and local 3-dimensional holonomy based on a 2-crossed module
Publication TypeUnpublished
Year of Publication2010
AuthorsMartins JF, Picken R
Series TitlePreprint
Palavras-chave2-crossed module, 3-dimensional holonomy, crossed square, Gray 3-groupoid, Higher Gauge Theory, Wilson 3-sphere
AbstractWe define the thin fundamental Gray 3-groupoid S3(M) of a smooth manifold M and define (by using differential geometric data) 3-dimensional holonomies, to be smooth strict Gray 3-groupoid maps S3(M) → C(H), where H is a 2-crossed module of Lie groups and C(H) is the Gray 3-groupoid naturally constructed from H. As an application, we define Wilson 3-sphere observables.
URLhttp://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2010/20_10.pdf