Occupants in simplicial complexes

Tillmann, Steffen

doi:10.2140/agt.2019.19.1265

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Occupants in simplicial complexes

Steffen Tillmann

Algebraic & Geometric Topology 19 (2019) 1265–1298

DOI: 10.2140/agt.2019.19.1265

Abstract

Let $M$ be a smooth manifold and $K \subset M$ be a simplicial complex of codimension at least $3$ . Functor calculus methods lead to a homotopical formula of $M ∖ K$ in terms of spaces $M ∖ T$ where $T$ is a finite subset of $K$ . This is a generalization of the author’s previous work with Michael Weiss (Contemp. Math. 682, Amer. Math. Soc., Providence, RI (2017) 237–259), where the subset $K$ is assumed to be a smooth submanifold of $M$ and uses his generalization of manifold calculus adapted for simplicial complexes.

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Keywords

calculus of functors, manifolds, simplicial complexes, complements

Mathematical Subject Classification 2010

Primary: 57R19

Secondary: 55P65

References

Publication

Received: 2 November 2017

Revised: 28 August 2018

Accepted: 13 September 2018

Published: 21 May 2019

Authors

Steffen Tillmann
Mathematisches Institut Westfälische Wilhelms-Universität Münster Münster Germany

Volume 19, issue 3 (2019)