Rational homological stability for groups of symmetric automorphisms of free groups
Abstract
Let Fn be the free group of rank n, with generating set S=\x1,...,xn\. An automorphism φ of Fn is called symmetric if for each 1≤ i≤ n, φ(xi) is conjugate to xj or xj-1 for some 1≤ j≤ n. Let Aut(Fn) be the group of symmetric automorphisms. We prove that the inclusion Aut(Fn) → Aut(Fn+1) induces an isomorphism in rational homology for n>(3i-1)/2.
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