For n≥3, the natural map Out(Fn)→Aut(Kn) from the outer automorphism group of the free group of rank n to the group of simplicial automorphisms of the spine of outer space is an isomorphism.
Duke Math. J.
106(2):
391-409
(1 February 2001).
DOI: 10.1215/S0012-7094-01-10625-X
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