Some classes of homeomorphisms that preserve multiplicity and tangent cones

Abstract

In this paper it is presented some classes of homeomorphisms that preserve multiplicity and tangent cones of complex analytic sets. Moreover, we present a class of homeomorphisms that has the multiplicity as an invariant when we consider right equivalence and this class contains many known classes of homeomorphisms that preserve tangent cones. Finally, we show versions of these results looking at infinity.