Abstract:

Let X be the germ of a complex-analytic space. In the smooth case X is (analytically) rectifiable to (C^n,o). Singular germs are much more complicated, with rich topology and geometry. Their study begins with the conic structure theorem: X is homeomorphic to Cone[Link[X]].

In "most cases" this homeomorphism cannot be chosen differentiable. A weaker question is to detect a bi-Lipschitz equivalence. The first obstruction to such bi-Lipschitzness are "fast cycles" on Link[X].

I will introduce the main players and then show "exotic Lipschitz structures". E.g., countable families of germs of topological manifolds, of distinct Lipschitz types, all realizable by algebraic hypersurfaces.

joint work with R. Mendes Pereira

Panopto link: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=2f598b0b-2c3f-4cad-b5be-b3cf00686e86