Representation stability on the cohomology of complements of subspace arrangements

2017/11/24 by Artur Rapp, Rapp, Artur
Mathematics · #05E05 #05E45 #20C30 #55R80 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Representation Theory (math.RT) #math.CO #math.GT #math.RT #msc:05E05 #msc:05E45 #msc:20C30 #msc:55R80

paper · pdf · doi:10.48550/arxiv.1711.08924

arxiv created 2017/11/24 · arxiv updated 2017/11/27

Abstract

We study representation stability in the sense of Church and Farb of sequences of cohomology groups of complements of arrangements of linear subspaces in real and complex space as S_n-modules. We consider arrangement of linear subspaces defined by sets of diagonal equalities x_i = x_j and invariant under the action of S_n permuting the coordinates. We provide bounds on the point when stabilization occurs and an alternative proof for the fact that stabilization happens. The latter is a special case of a very general stabilization result of Gadish and for the pure braid space the result is part of the work of Church and Farb. For this space better stabilization bounds were obtained by Hersh and Reiner.

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