Representation stability for the cohomology of the pure string motion groups

Details Representation stability for the cohomology of the pure string motion groups Representation stability for the cohomology of the pure string motion groups

2011-08-05

arxiv.org/abs/1108.1255v2

Mathematics

Geometric Topology

24 pages, 3 figures

Scientific paper

The cohomology of the pure string motion group PSigma_n admits a natural action by the hyperoctahedral group W_n. In recent work, Church and Farb conjectured that for each k > 0, the sequence of degree k rational cohomology groups of PSigma_n is uniformly representation stable with respect to the induced action by W_n, that is, the description of the groups' decompositions into irreducible W_n representations stabilizes for n >> k. We use a characterization of the cohomology groups 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 vanish in positive degree. We also prove that the subgroup of orientation-preserving string motions, also known as the braid-permutation group, is rationally cohomologically stable in the classical sense.

Affiliated with

Also associated with

No associations

Rating

Representation stability for the cohomology of the pure string motion groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Representation stability for the cohomology of the pure string motion groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Representation stability for the cohomology of the pure string motion groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-668094