Cohomology of automorphism groups of free groups with twisted coefficients

• Oscar Randal-Williams ^[1]
  1. [1] Centre for Mathematical Sciences
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 2, 2018, págs. 1453-1478
• Idioma: inglés
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• Resumen

  • We compute the groups H∗(Aut(Fn);M) and H∗(Out(Fn);M) in a stable range, where M is obtained by applying a Schur functor to HQ or H∗Q , respectively the first rational homology and cohomology of Fn . The answer may be described in terms of stable multiplicities of irreducibles in the plethysm Symk∘Syml of symmetric powers. We also compute the stable integral cohomology groups of Aut(Fn) with coefficients in H or H∗ .