The fundamental Gray 3-groupoid of a smooth manifold and local 3-dimensional holonomy based on a 2-crossed module |
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| Authors: | João Faria Martins Roger Picken |
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| Institution: | a Departamento de Matemática, Faculdade de Ciências e Tecnologia (Universidade Nova de Lisboa), Quinta da Torre, 2829-516 Caparica, Portugal
b Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento de Matemática, Instituto Superior Técnico (Universidade Técnica de Lisboa), Av. Rovisco Pais, 1049-001 Lisboa, Portugal |
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| Abstract: | We 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. |
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| Keywords: | primary 53C29 secondary 18D05 70S15 |
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