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2012 Representation stability for the cohomology of the pure string motion groups
Jennifer Wilson
Algebr. Geom. Topol. 12(2): 909-931 (2012). DOI: 10.2140/agt.2012.12.909


The cohomology of the pure string motion group PΣn admits a natural action by the hyperoctahedral group Wn. In recent work, Church and Farb conjectured that for each k1, the cohomology groups Hk(PΣn;) are uniformly representation stable; that is, the description of the decomposition of Hk(PΣn;) into irreducible Wn–representations stabilizes for n>>k. We use a characterization of H(PΣn;) given by Jensen, McCammond and Meier to prove this conjecture. Using a transfer argument, we further deduce that the rational cohomology groups of the string motion group Hk(Σn;) vanish for k1. We also prove that the subgroup of Σn+Σn of orientation-preserving string motions, also known as the braid-permutation group, is rationally cohomologically stable in the classical sense.


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Jennifer Wilson. "Representation stability for the cohomology of the pure string motion groups." Algebr. Geom. Topol. 12 (2) 909 - 931, 2012.


Received: 11 August 2011; Accepted: 19 December 2011; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1282.20059
MathSciNet: MR2928898
Digital Object Identifier: 10.2140/agt.2012.12.909

Primary: 20C15, 20J06
Secondary: 20F28, 57M25

Rights: Copyright © 2012 Mathematical Sciences Publishers


Vol.12 • No. 2 • 2012
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