Manifold calculus adapted for simplicial complexes

2017/02/18 by Tillmann, Steffen
#Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1702.05608

Abstract

We develop a generalization of manifold calculus in the sense of Goodwillie-Weiss where the manifold is replaced by a simplicial complex. We consider functors from the category of open subsets of a fixed simplical complex into the category of topological spaces and prove an analogue of the approximation theorem. Namely, under certain conditions such a functor can be approximated by a tower of (appropriately adapted) polynomial functors.

Related

• Introduction to the manifold calculus of Goodwillie-Weiss
• Multivariable manifold calculus of functors
• A Context for Manifold Calculus
• Classification of polynomial functors in manifold calculus, Part I
• Special Open Sets in Manifold Calculus