Local holomorphic dynamics

seminar: Topological aspects of singularities of holomorphic foliations in the plane

speaker: David Marín (Departament de Matemàtiques, Universitat Autònoma de Barcelona)

abstract: In this talk we deal with the problem of topological classification of singular holomorphic vector fields $X$ in a neighbordhood $U$ of the origin in $\mathbb{C}^2$. We begin with the (quasi) homogeneous case (TQH), in which the reduction of the singularity is achived after a single (quasi-homogeneous sequence of) blowing-up. The key result is the topological invariance of the holonomy, which remains an open problem in the general setting. In order to treat it, we present some ideas that we hope will be useful. First, we can consider a (JSJ) decomposition the complementary set $U\setminus S$ of the separatrices $S$ of $X$ into pieces of TQH type. In order to combine this merely topological result with the geometric data given by $X$ we need to use a recent result, obtained in collaboration with J.-F. Mattei, implying that each leaf of $X$ is incompressible in $U\setminus S$.

timetable:
Mon 22 Jan, 16:00 - 17:00, Aula Dini
documents:

Topological aspects of singularities of holomorphic foliations in the plane

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