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arXiv · 0904.4185

Multivariable manifold calculus of functors

Brian A. Munson·Ismar Volic
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Abstract

Manifold calculus of functors, due to M. Weiss, studies contravariant functors from the poset of open subsets of a smooth manifold to topological spaces. We introduce "multivariable" manifold calculus of functors which is a generalization of this theory to functors whose domain is a product of categories of open sets. We construct multivariable Taylor approximations to such functors, classify multivariable homogeneous functors, apply this classification to compute the derivatives of a functor, and show what this gives for the space of link maps. We also relate Taylor approximations in single variable calculus to our multivariable ones.

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Brian A. Munson, Ismar Volic. 2010-09-10. Multivariable manifold calculus of functors. https://arxiv.org/abs/0904.4185

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