The Euler Characteristic of the Whitehead Automorphism Group of a Free Product
نویسنده
چکیده
A combinatorial summation identity over the lattice of labelled hypertrees is established that allows one to gain concrete information on the Euler characteristics of various automorphism groups of free products of groups. In particular, we establish formulae for the Euler characteristics of: the group of Whitehead automorphisms Wh(∗ i=1 Gi) when the Gi are of finite homological type; Aut(∗ i=1 Gi) and Out(∗ n i=1 Gi) when the Gi are finite; and the palindromic automorphism groups of finite rank free groups.
منابع مشابه
Decorated hypertrees
C. Jensen, J. McCammond and J. Meier have used weighted hypertrees to compute the Euler characteristic of a subgroup of the automorphism group of a free product. Weighted hypertrees also appear in the study of the homology of the hypertree poset. We link them to decorated hypertrees after a general study on decorated hypertrees, which we enumerate using box trees.
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C. Jensen, J. McCammond and J. Meier have used weighted hypertrees to compute the Euler characteristic of a subgroup of the automorphism group of a free product. Weighted hypertrees also appear in the study of the homology of the hypertree poset. We link them to decorated hypertrees after a general study on decorated hypertrees, which we enumerate using box trees.
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تاریخ انتشار 2004