AN AXIOMATIC DEFINITION OF HOLONOMY-Reference-Cited by-同舟云学术

AN AXIOMATIC DEFINITION OF HOLONOMY

Published:1994-12 Issue:06 Volume:05 Page:835-848
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

CAETANO A.¹²,PICKEN R. F.³⁴

Affiliation:

1. Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, R. Ernesto de Vasconcelos, Bloco C1, 1700 Lisboa, Portugal

2. Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1699 Lisboa Codex, Portugal

3. Departamento de Matemática, Instituto Superior Técnico, Avenida Rovisco Pais, 1096 Lisboa Codex, Portugal

4. Centro de Física da Matéria Condensada, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1699 Lisboa Codex, Portugal

Abstract

A group of loops [Formula: see text] is associated to every smooth pointed manifold M using a strong homotopy relation. It is shown that the holonomy of a connection on a principal G-bundle may be presented as a group morphism [Formula: see text] and that every such morphism satisfying a natural smoothness condition is the holonomy of some unique connection up to isomorphism.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X94000425

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