Rational homological stability for groups of symmetric automorphisms of free groups
arXiv:1111.6506
Abstract
Let F_n be the free group of rank n, with generating set S=\{x_1,...,x_n\}. An automorphism ϕof F_n is called symmetric if for each 1\leq i\leq n, ϕ(x_i) is conjugate to x_j or x_j^{-1} for some 1\leq j\leq n. Let ΣAut(F_n) be the group of symmetric automorphisms. We prove that the inclusion ΣAut(F_n) \rightarrow ΣAut(F_{n+1}) induces an isomorphism in rational homology for n>(3i-1)/2.
Results subsumed by arXiv:1203.4845. Minor edits, references updated. 8 pages