Smooth maps, pullback path spaces, connections, and torsions

Chen, Kuo Tsai

doi:10.1090/S0002-9947-1986-0854088-1

Smooth maps, pullback path spaces, connections, and torsions
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Trans. Amer. Math. Soc. 297 (1986), 617-627 Request permission

Abstract:

By generalizing the local version of the usual differential geometric notion of connections and that of torsions, a model for the pullback path space of a smooth map is constructed from the induced map of the de Rham complexes. The pullback path space serves not only as a homotopy fiber but also as a device reflecting differentiable properties of the smooth map. Applications are discussed.

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