Smooth Homotopy of Infinite-Dimensional $C^{\infty }$-Manifolds Harry Fletcher-Wood maintaining aspects of independent living

maintaining aspects of independent living

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Smooth Homotopy of Infinite-Dimensional $C^{\infty }$-Manifolds Harry Fletcher-Wood maintaining aspects of independent livingIn this paper, we use homotopical algebra (or abstract homotopical methods) to study smooth homotopical problems of infinite dimensional C$C^{\infty }$ manifolds in convenient calculus. More precisely, we discuss the smoothing of maps, sections, principal bundles, and gauge transformations. We first introduce the notion of hereditary C$C^{\infty }$ paracompactness along with the semiclassicality condition on a C$C^{\infty }$ manifold, which enables us