Seminario teoría de grupos UAM-ICMAT

María Pe Pereira

(Universidad Complutense de Madrid)

"Curve monodromy, quasi-periodic diffeomorphism and tête-à-tête graphs"

Lunes 29/1/2018, 14:30, Aula 520, UAM

Resumen: I will report about a joint work with J. Fernández de Bobadilla and P. Portilla
which is also part of the PhD Thesis of the third author.
Norbert A’Campo defined tête-à-tête graphs and showed that if the monodromy
of a plane branch is periodic then it is a generalized Dehn twist along a tête-à-tête
graph.
We see that any periodic orientable diffeomorphisms of surfaces with non-empty
boundary is induced by a generalized Dehn twist along a tête-à-tête graph. In this
sense we generalize a result by Christian Graf.
We also study the more general case of quasi-periodic homeomorphisms of sur-
faces with boundary. Monodromy of an arbitrary plane curve is an example of
them. To codify this type of homeomorphisms we introduce the notion of mixed
tête-à-tête graph, improving a former version by A’Campo. We show that any
quasi periodic homeomorphism, subject to certain combinatorial restriction, can
be modelized with a mixed tête-à-tête graph. These restrictions are accomplished
by the monodromy of unibranch plane curves.
In this talk I will introduce the monodromy of plane branches, the quasi-periodic
automorpisms, the tête-à-tête graphs and the mentioned characterizations.