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2016 Homotopy groups of diagonal complements
Sadok Kallel, Ines Saihi
Algebr. Geom. Topol. 16(5): 2949-2980 (2016). DOI: 10.2140/agt.2016.16.2949

Abstract

For X a connected finite simplicial complex we consider Δd(X,n), the space of configurations of n ordered points of X such that no d + 1 of them are equal, and Bd(X,n), the analogous space of configurations of unordered points. These reduce to the standard configuration spaces of distinct points when d = 1. We describe the homotopy groups of Δd(X,n) (resp. Bd(X,n)) in terms of the homotopy (resp. homology) groups of X through a range which is generally sharp. It is noteworthy that the fundamental group of the configuration space Bd(X,n) abelianizes as soon as we allow points to collide, ie d 2.

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Sadok Kallel. Ines Saihi. "Homotopy groups of diagonal complements." Algebr. Geom. Topol. 16 (5) 2949 - 2980, 2016. https://doi.org/10.2140/agt.2016.16.2949

Information

Received: 22 September 2015; Revised: 15 January 2016; Accepted: 7 February 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1355.55012
MathSciNet: MR3572355
Digital Object Identifier: 10.2140/agt.2016.16.2949

Subjects:
Primary: 55Q52
Secondary: 55P10

Rights: Copyright © 2016 Mathematical Sciences Publishers

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