Michael Handel

Laminations, trees, and irreducible automorphisms of free groups

Abstract. We examine the action of Out(Fn) on the set of (irreducible) laminations. Consequences include a special case of the Tits alternative for Out(Fn), the discreteness of certain naturally arising group actions on trees, and word hyperbolicity of certain semidirect products.

The Tits alternative for Out (F~n) I: Dynamics of exponentially-growing automorphisms

The Tits alternative for Out(F_n) is reduced to the case where all elements in the subgroup under consideration grow polynomially.

Periodic points of Hamiltonian surface diffeomorphisms

The main result of this paper is that every non-trivial Hamiltonian dieomor- phism of a closed oriented surface of genus at least one has periodic points of arbitrarily high period. The same result is true for S 2 provided the dif- feomorphism has at least three xed points. In addition we show that up to isotopy relative to its xed point set, every orientation preserving dieomor- phism F : S! S of a closed orientable surface has a normal form. If the xed point set is nite this is just the Thurston normal form.

The free splitting complex of a free group, I Hyperbolicity

We prove that the free splitting complex of a finite rank free group, also known as Hatchers sphere complex, is hyperbolic.

Distortion elements in group actions on surfaces

If

The rotation set of a homeomorphism of the annulus is closed

\G

The Recognition Theorem for Out(Fn)

is a finitely generated group with generators

The forcing partial order on the three times punctured disk

\{g_1,...,g_j\}

The expansion factors of an outer automorphism and its inverse

then an infinite order element

Area preserving group actions on surfaces

f \in \G