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Tête-à-tête twists, monodromies and representation of elements of Mapping Class Group

2022; Association of the Annals of the Fourier Institute; Volume: 71; Issue: 6 Linguagem: Inglês

10.5802/aif.3459

1777-5310

Norbert A’Campo, Javier Fernández de Bobadilla, María Pe Pereira, Pablo Portilla Cuadrado,

Advanced Scientific Research Methods

We study monodromies of plane curve singularities and pseudo-periodic homeomorphisms of oriented surfaces with boundary using tête-à-tête graphs and twists. A tête-à-tête twist is a generalisation of the classical Dehn twist. We introduce the class of mixed tête-à-tête graphs and twists, and prove that mixed tête-à-tête twists contain the monodromies of irreducible plane curve singularities. In a sequel paper, the fourth author and B. Sigurdsson have extended this to the reducible case.