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The cohomology groups of the outer Whitehead automorphism group of a free product

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Published/Copyright: February 8, 2010
Forum Mathematicum
From the journal Volume 22 Issue 2

Abstract

Let Γ = G1 ∗ G2 ∗ ⋯ ∗ Gn be an n-fold free product. For gi ∈ Gi and gk ∈ Gk, let be the automorphism induced by

where means conjugating gk by gj). Then is a Whitehead automorphism, and the group generated by all is known at the Whitehead automorphism group of Γ, denoted Wh(Γ). In this paper, we calculate H*(Wh(Γ)). The main tools used are the action of Wh(Γ) on a space constructed by McCullough-Miller and the equivariant spectral sequence. We also specialize to the case of Γ a free Coxeter group, where further analysis allows us to determine a presentation for the cohomology ring.

Received: 2008-05-20
Revised: 2008-07-01
Published Online: 2010-02-08
Published in Print: 2010-March

© de Gruyter 2010

Articles in the same Issue

  1. Lp estimates for parabolic magnetic Schrödinger operators
  2. Calculation of UNil for the cyclic group of order two
  3. Lie theoretic significance of the measure topologies associated with a finite trace
  4. Integral formulas for a class of curvature PDE's and applications to isoperimetric inequalities and to symmetry problems
  5. The finiteness of NK1(ℤ[G])
  6. Poincaré duality pairs of dimension three
  7. Optimal quantization of probabilities concentrated on small balls
  8. A sharp diameter bound for unipotent groups of classical type over ℤ/pℤ
  9. Homological localizations of Eilenberg–MacLane spectra
  10. A∞-coalgebra structure maps that vanish on H∗(K(π, n); ℤp)
  11. The cohomology groups of the outer Whitehead automorphism group of a free product
  12. Dual topology of the motion groups
https://doi.org/10.1515/forum.2010.021

Articles in the same Issue

  1. Lp estimates for parabolic magnetic Schrödinger operators
  2. Calculation of UNil for the cyclic group of order two
  3. Lie theoretic significance of the measure topologies associated with a finite trace
  4. Integral formulas for a class of curvature PDE's and applications to isoperimetric inequalities and to symmetry problems
  5. The finiteness of NK1(ℤ[G])
  6. Poincaré duality pairs of dimension three
  7. Optimal quantization of probabilities concentrated on small balls
  8. A sharp diameter bound for unipotent groups of classical type over ℤ/pℤ
  9. Homological localizations of Eilenberg–MacLane spectra
  10. A∞-coalgebra structure maps that vanish on H∗(K(π, n); ℤp)
  11. The cohomology groups of the outer Whitehead automorphism group of a free product
  12. Dual topology of the motion groups
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