Homology, Homotopy and Applications

Volume 21 (2019)

Number 1

Manifold calculus adapted for simplicial complexes

Pages: 161 – 186

DOI: https://dx.doi.org/10.4310/HHA.2019.v21.n1.a8


Steffen Tillmann (Mathematisches Institut, Universität Münster, Germany)


We develop a generalization of Goodwillie–Weiss manifold calculus to the setting of simplicial complexes. We consider functors from the category of open subsets of a fixed simplicial complex into the category of topological spaces and prove that in many cases such a functor can be approximated by a tower of polynomial functors. Applications include the study of configuration spaces and other complements, spaces of immersions with prescribed singularities or embeddings of singular spaces.


calculus of functors, simplicial complex, embedding

2010 Mathematics Subject Classification

57R40, 57R42, 57R55

Received 18 February 2017

Received revised 4 April 2017

Published 26 September 2018