Geodesic
Homotopy groups of diagonal complements
Kallel, Sadok1 ; Saihi, Ines2
1Department of Mathematics, American University of Sharjah, Sharjah, United Arab Emirates
2Ecole nationale supérieure d’ingénieurs de Tunis, Université de Tunis, 05, Avenue Taha Hussein, 1008 Montfleury, Tunisia, Laboratoire LATAO, Faculté des sciences de Tunis, Université de Tunis-El Manar
Algebraic and Geometric Topology, Tome 16 (2016) no. 5, pp. 2949-2980
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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.

DOI : 10.2140/agt.2016.16.2949
Classification : 55Q52, 55P10
Keywords: diagonal arrangements, homotopy groups, configuration spaces, colimit diagram

Kallel, Sadok  1   ; Saihi, Ines  2

1 Department of Mathematics, American University of Sharjah, Sharjah, United Arab Emirates
2 Ecole nationale supérieure d’ingénieurs de Tunis, Université de Tunis, 05, Avenue Taha Hussein, 1008 Montfleury, Tunisia, Laboratoire LATAO, Faculté des sciences de Tunis, Université de Tunis-El Manar 
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Kallel, Sadok; Saihi, Ines. Homotopy groups of diagonal complements. Algebraic and Geometric Topology, Tome 16 (2016) no. 5, pp. 2949-2980. doi: 10.2140/agt.2016.16.2949

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