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arXiv · 1111.6506

Rational homological stability for groups of symmetric automorphisms of free groups

Matthew C. B. Zaremsky
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Abstract

Let F_n be the free group of rank n, with generating set S=\{x_1,...,x_n\}. An automorphism \phi of F_n is called symmetric if for each 1\leq i\leq n, \phi(x_i) is conjugate to x_j or x_j^{-1} for some 1\leq j\leq n. Let \Sigma Aut(F_n) be the group of symmetric automorphisms. We prove that the inclusion \Sigma Aut(F_n) \rightarrow \Sigma Aut(F_{n+1}) induces an isomorphism in rational homology for n>(3i-1)/2.

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Matthew C. B. Zaremsky. 2011-11-28. Rational homological stability for groups of symmetric automorphisms of free groups. https://arxiv.org/abs/1111.6506

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