%0 Journal Article
%T Multivariable manifold calculus of functors
%A Brian A. Munson
%A Ismar Volic
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0904.4185v2