2009/04/27 by Brian A. Munson, Munson, Brian A., Ismar Volić +2
Mathematics · #57Q45 #57R40 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT #msc:57Q45 #msc:57R40
paper · pdf · doi:10.48550/arxiv.0904.4185
37 pages
openalex publication_date 2009/04/27 · arxiv created 2010/09/10 · arxiv updated 2010/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.