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arXiv · 1706.05580

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

Norbert A'Campo·Javier Fernandez de Bobadilla·Maria Pe Pereira·Pablo Portilla Cuadrado
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Abstract

We study monodromies of plane curve singularities and pseudo-periodic homeomorphisms of oriented surfaces with boundary, following an original idea of the first author: tête-à-tête graphs and twists. We completely characterize mapping classes that can be represented by tête-à-tête twists, and generalize the notion to be able to represent any class of the mapping class group relative to the boundary which is boundary-free periodic. This improves previous work on the subject by C. Graf. Furthermore, we introduce the class of mixed tête-à-tête graphs and twists, and prove that mixed tête-à-tête twists contain monodromies of irreducible plane curve singularities. In a sequel paper, the fourth author and B. Sigurdsson have extended this to the reducible case.

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Norbert A'Campo, Javier Fernandez de Bobadilla, Maria Pe Pereira, Pablo Portilla Cuadrado. 2019-12-26. Tête-à-tête twists, monodromies and representation of elements of Mapping Class Group. https://arxiv.org/abs/1706.05580

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