A topological introduction to Lipschitz geometry of complex singularities
Winter Braids IX (Reims, 2019), Winter Braids Lecture Notes (2019), Talk no. 3, 17 p.

These are the notes of the three lectures I gave during the IXth Winterbraids School which took place in Reims from 4 to 7th March 2019. The aim of this course was to introduce researchers working in low-dimensional topology to Lipschitz geometry of complex singularities. In these lectures, I focussed on topological points of view on the objects, avoiding as much as possible technical material from algebraic geometry and singularity theory such as resolution of singularities, Nash transform, generic projections of curves and surfaces, etc.

It starts with an introduction to Lipschitz geometry of singular spaces. It then gives the complete classification of Lipschitz geometry of complex curves and covers the result of [17]. The last part is an introduction to Lipschitz geometry of complex surfaces and states the thick-thin decomposition Theorem of a normal complex surface proved in [6].

DOI: 10.5802/wbln.29
Pichon, Anne 1

1 Aix Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France
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Pichon, Anne. A topological introduction to Lipschitz geometry of complex singularities, in Winter Braids IX (Reims, 2019), Winter Braids Lecture Notes (2019), Talk no. 3, 17 p. doi : 10.5802/wbln.29. http://archive.numdam.org/articles/10.5802/wbln.29/

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