A characterization of Whitney a-regular complex analytic stratifications

TL;DR

This paper establishes that the openness of certain transverse maps implies Whitney a-regularity of complex analytic stratifications, extending Trotman's theorem into the complex setting.

Contribution

It proves a complex analogue of Trotman's theorem, linking the openness of transverse maps to Whitney a-regularity of stratifications in complex analytic geometry.

Findings

Openness of transverse maps implies Whitney a-regularity.

Extension of Trotman's theorem to complex analytic stratifications.

Provides a new criterion for Whitney a-regularity in complex geometry.

Abstract

We prove that the openness of the set of maps, between a Stein manifold and an Oka manifold, transverse to a stratification of a complex analytic subvariety in the target implies that the stratification is Whitney $a$-regular. Our result can be seen as a complex version of Trotman's theorem.