Noticias Destacadas
 Agenda del Departamento |
- Información (provisional) sobre grupos y horarios de las asignaturas impartidas por el Departamento de Matemáticas, para el curso 2023-2024.
- Propuestas de Trabajos de Fin de Grado para el curso 2023-2024.
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Canal @matematicasuamEnlace al canal del Departamento en youtube. |
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PIM (Pequeño Instituto de Matemáticas)Con el objetivo de fomentar el interés por las matemáticas y dirigido a jóvenes entre 14 y 18 años, nace este proyecto de Instituto de Ciencias Matemáticas (ICMAT) en colaboración con nuestro Departamento, la Universidad Autónoma de Madrid y la Real Sociedad Matemática Española. El proyecto comienzó en el curso académico 2022-2023. Ampliar información en su página web. |
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Seminario Teoría de Grupos
CURVE MONODROMY, QUASI-PERIODIC DIFFEOMORPHISMS AND TETE-A-TETE GRAPHS.
MARÍA PE PEREIRA
UCM
Jueves 18 de enero, 14:30 hr.
Aula 520, módulo 17
Resumen: I will report about a joint work with J. Fern ́andez de Bobadilla and P. Portilla
which is also part of the PhD Thesis of the third author.
Norbert A’Campo defined tête-a-tête graphs and showed that if the monodromy
of a plane branch is periodic then it is a generalized Dehn twist along a tête-a-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-a-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-a-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-a-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-a-tête graphs and the mentioned characterizations.