Multiplicity of analytic hypersurface singularities under bi-Lipschitz homeomorphisms

Abstract

We give partial answers to a metric version of Zariski's multiplicity conjecture. In particular, we prove the multiplicity of complex analytic surface (not necessarily isolated) singularities in ${\mathbb{C}}^3$ is a bi-Lipschitz invariant.

Accepted for publication by the Journal of Topology

References in corpus (1)

• Thin-thick decomposition for real definable isolated singularities

Cited by in corpus (3)

• Multiplicity and degree as bi-Lipschitz invariants for complex sets
• Multiplicity of singularities is not a bi-Lipschitz invariant
• Moderately Discontinuous Homotopy