The Euler characteristic of the Whitehead automorphism group of a free product

Jensen, Craig; McCammond, Jon; Meier, John

doi:10.1090/S0002-9947-07-03967-0

The Euler characteristic of the Whitehead automorphism group of a free product
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by Craig Jensen, Jon McCammond and John Meier PDF

Trans. Amer. Math. Soc. 359 (2007), 2577-2595 Request permission

Abstract:

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 $\mathrm {Wh}(\ast _{i=1}^n G_i)$ when the $G_i$ are of finite homological type; $\operatorname {Aut}(\ast _{i=1}^n G_i)$ and $\operatorname {Out} (\ast _{i=1}^n G_i)$ when the $G_i$ are finite; and the palindromic automorphism groups of finite rank free groups.

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