TITLE: Parageometric automorphisms of free groups (joint work with Michael
Handel)



Abstract: Infinite order, irreducible automorphisms of surface groups have
particularly nice invertible topological representatives, namely,
pseudo-Anosov homeomorphisms. Infinite order, irreducible automorphisms of
free groups, with irreducible powers, have nice noninvertible topological
representatives, namely, train track maps; moreover, if the automorphism
is "geometric" then it also has a nice invertible representative, namely,
a pseudo-Anosov homeomorphism of a one-holed surface. We describe
"parageometric" automorphisms, which also have nice invertible
representatives, but with somewhat weirder properties than pseudo-Anosov
homeomorphisms. For example, the expansion factor of a parageometric
automorphism is strictly greater than the expansion factor of its inverse;
as a consequence, the inverse of a parageometric automorphism is neither
geometric nor parageometric.