## Multiplicity modulo two as a metric invariant

Guillaume Valette

Polish Academy of Science

Abstract

The multiplicity of a real analytic hypersurface defined by a reduced analytic equation P = 0, is the lowest homogeneous degree in the Taylor expansion of P . Modulo \(2\) it is independent of the chosen reduced equation. This talk will address the following question: Is multiplicity modulo \(2\) a metric invariant ? I will give some partial answers.