Rational homological stability for groups of symmetric automorphisms of free groups

Details Rational homological stability for groups of symmetric automorphisms of free groups Rational homological stability for groups of symmetric automorphisms of free groups

2011-11-28

arxiv.org/abs/1111.6506v3

Mathematics

Group Theory

Results subsumed by arXiv:1203.4845. Minor edits, references updated. 8 pages

Scientific paper

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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