Kuo Tsai Chen, Smooth maps, pullback path spaces, connections, and torsions, Trans. Amer. Math. Soc. 297 (1986) 617–627 (web)
T. Kohno, Higher holonomy maps for hyperplane arrangements, European J. Math. 6, 905–927 (2020) doi
We develop a method to construct representations of the homotopy 2-groupoid of a manifold as a 2-category by means of Chen’s formal homology connections. As an application we describe 2-holonomy maps for hyperplane arrangements and discuss representations of the category of braid cobordisms.
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