Die Isomorphismengruppe der freien Gruppen

Dimension of the Torelli group for Out(Fn)

“…We remark that T 1 is obviously trivial and T 2 is trivial by a classical result of Nielsen [11] (we give a new proof of the latter fact in Section 5).…”

“…It is a theorem of Nielsen that this map is surjective [11]. We call its kernel the Torelli subgroup of Out(F n ), and we denote it by T n :…”

Groups with the Same lower Central Sequence as a Relatively Free Group. II. Properties

“…is a proper subgroup of Fl+1 for i'=l, 2, -Note that if Fis a free group of rank two on a and b and if u e y2F, then au and b generate F if and only if u = [a, V] for some i (this follows immediately from a theorem of J. Nielsen [30]). This makes the choice of ut particularly easy.…”

Imbeddings of free actions on handlebodies

“…An equivalence j : V 1 → V 2 between the actions induces a homeomorphism j : [5]), all of Nielsen's [7] generators of the automorphism group of the free group π 1 (W 2 ) can be induced by homeomorphisms, so f may be selected to induce Ψ. The condition that φ 2 •Ψ = φ 1 then shows that f lifts to a homeomorphism of covering spaces j : V 1 → V 2 , and moreover, ensures that h(x) = j −1 (h(j(x))).…”