Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 16, Number 5 (2016), 2949-2980.
Homotopy groups of diagonal complements
For a connected finite simplicial complex we consider , the space of configurations of ordered points of such that no of them are equal, and , the analogous space of configurations of unordered points. These reduce to the standard configuration spaces of distinct points when . We describe the homotopy groups of (resp. ) in terms of the homotopy (resp. homology) groups of through a range which is generally sharp. It is noteworthy that the fundamental group of the configuration space abelianizes as soon as we allow points to collide, ie .
Algebr. Geom. Topol., Volume 16, Number 5 (2016), 2949-2980.
Received: 22 September 2015
Revised: 15 January 2016
Accepted: 7 February 2016
First available in Project Euclid: 16 November 2017
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Kallel, Sadok; Saihi, Ines. Homotopy groups of diagonal complements. Algebr. Geom. Topol. 16 (2016), no. 5, 2949--2980. doi:10.2140/agt.2016.16.2949. https://projecteuclid.org/euclid.agt/1510841235