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2003 Finite subset spaces of graphs and punctured surfaces
Christopher Tuffley
Algebr. Geom. Topol. 3(2): 873-904 (2003). DOI: 10.2140/agt.2003.3.873


The kth finite subset space of a topological space X is the space expk(X) of non-empty finite subsets of X of size at most k, topologised as a quotient of Xk. The construction is a homotopy functor and may be regarded as a union of configuration spaces of distinct unordered points in X. We calculate the homology of the finite subset spaces of a connected graph Γ, and study the maps (expk(ϕ)) induced by a map ϕ:ΓΓ between two such graphs. By homotopy functoriality the results apply to punctured surfaces also. The braid group Bn may be regarded as the mapping class group of an n–punctured disc Dn, and as such it acts on H(expk(Dn)). We prove a structure theorem for this action, showing that the image of the pure braid group is nilpotent of class at most (n1)2.


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Christopher Tuffley. "Finite subset spaces of graphs and punctured surfaces." Algebr. Geom. Topol. 3 (2) 873 - 904, 2003.


Received: 21 February 2003; Revised: 16 September 2003; Accepted: 23 September 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1032.55014
MathSciNet: MR2012957
Digital Object Identifier: 10.2140/agt.2003.3.873

Primary: 54B20
Secondary: 05C10, 20F36, 55Q52

Rights: Copyright © 2003 Mathematical Sciences Publishers


Vol.3 • No. 2 • 2003
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