Volume 19, issue 3 (2019)

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Occupants in simplicial complexes

Steffen Tillmann

Algebraic & Geometric Topology 19 (2019) 1265–1298

Let M be a smooth manifold and K 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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calculus of functors, manifolds, simplicial complexes, complements
Mathematical Subject Classification 2010
Primary: 57R19
Secondary: 55P65
Received: 2 November 2017
Revised: 28 August 2018
Accepted: 13 September 2018
Published: 21 May 2019
Steffen Tillmann
Mathematisches Institut
Westfälische Wilhelms-Universität Münster