Translator Disclaimer
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

Abstract

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.

Citation

Download Citation

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

Information

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

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

Rights: Copyright © 2012 Mathematical Sciences Publishers

JOURNAL ARTICLE
23 PAGES


SHARE
Vol.12 • No. 2 • 2012
MSP
Back to Top