Topology Seminar: Jenny Wilson

  • Date: 04/02/2012
  • Time: 14:00
Lecturer(s):
Jenny Wilson
Location: 

University of British Columbia

Topic: 

The cohomology groups of the pure string motion group are uniformly representation stable

Description: 

Abstract

 

In the past two years, Church, Farb and others have developed the concept of 'representation stability', an analogue of homological stability for a sequence of groups or spaces admitting group actions. In this talk, I will give an overview of this new theory, using the pure string motion group P\Sigma_n as a motivating example. The pure string motion group, which is closely related to the pure braid group, is not cohomologically stable in the classical sense -- for each k>0, the dimension of the degree k rational cohomology of P\Sigma_n tends to infinity as n grows. The groups H^k(P\Sigma_n, \Q) are, however, representation stable with respect to a natural action of the hyperoctahedral group W_n -- that is, in some precise sense, the description of the decomposition of these cohomology groups into irreducible W_n-representations stabilizes for n>>k. I will outline a proof of this result, verifying a conjecture by Church and Farb. 

Other Information: 

Location: WMAX 110

 

For more information please visit UBC Math Department

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