An introduction to Lipschitz geometry of complex singularities

Anne Pichon (1)

1 I2M - Institut de Mathématiques de Marseille

The aim of this paper to introduce the reader to a recent point of view on the Lipschitz classifications of complex singularities. It presents the complete classification of Lipschitz geometry of complex plane curves singularities and in particular, it introduces the so-called bubble trick and bubble trick with jumps which are key tools to study Lipschitz geometry of germs. It describes also the thick-thin decomposition of a normal complex surface singularity and built two geometric decompositions of a normal surface germ into standard pieces which are invariant by respectively inner and outer bilipschitz homeomorphisms. This leads in particular to the complete classification of Lipschitz geometry for the inner metric.

Domaines: Géométrie algébrique [math.AG]

Anne Pichon. An introduction to Lipschitz geometry of complex singularities. Walter Neumann et Anne Pichon. Introduction to Lipschitz Geometry of Singularities, Lecture Notes of the International School on Singularity Theory and Lipschitz Geometry, Cuernavaca, June 2018, Lecture Notes in Mathematics (2280), Springer, 2021. ⟨hal-03168404⟩