Bubble tricks in Lipschitz geometry

Resumen:

I will explain how Lipschitz geometry of a complex plane curve determines its embedded topological type. The main argument is what we call a “bubble trick", which enable ones to explore the curve using balls centered at points along continuous arcs on the curve starting from the singular point and recover the multiplicity and the essential Puiseux exponents of the curve. This process is stable by bilipschitz change of the metric. l will also show how this point of view can be adapted to higher dimensions. In particular, it enables one to recover a large amount of the analytical data of a complex surface from its outer geometry. 

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