Invariants associated with blow-analytic homeomorphisms

Abstract

Blow-analytic equisingularity is a relatively young branch of mathematics, it has been developed over the last three decades. This paper answers some fundamental questions raised by Kuo-Milman [10] and Koike (private communication). We believe that the results we present here are of interest for those working in blow-analytic equisingularity. In particular we show that the singular loci of analytic functions germs, correspond even under arc-analytic equivalences. We also give easier proofs of some results in [1].