Orateur
Description
An important aspect of the theory of pseudo-Anosov mapping
classes concerns the study of the stretch factor lambda(f) of a
pseudo-Anosov mapping class f. This is a bi-Perron algebraic integer
of degree bounded above by 6g-6 which is the dimension of the
Teichmüller space for the underlying surface. The question of
realising any bi-Perron algebraic integer as a stretch factor is a
major challenge in the theory. Thurston, in his paper explaining his
famous construction of products of multitwists (popularized by a talk
of John Hubbard after a bouillabaisse at CIRM) claimed, without proof,
that the pseudo-Anosov maps obtained by this construction show that
the bound 6g-6 is sharp.
I will explain how to justify this claim and show that every even
degree between 2 and 6g-6 arises as the stretch factor degree of a
pseudo-Anosov mapping class in the Torelli group.
