Stable properties under weakly geometrically flat maps

TL;DR

This paper proves that weakly geometrically flat maps between complex spaces preserve certain local properties and allow cycle lifting, facilitating property transfer between spaces.

Contribution

It introduces the local cycle lifting property for weakly geometrically flat maps and demonstrates property transfer between complex spaces under these maps.

Findings

Weakly geometrically flat maps have the local cycle lifting property.

Properties of the domain space are transferred to the codomain.

The results apply to pure dimensional complex spaces.

Abstract

In this note we show that a weakly geometrically flat map $\pi$ : M $\rightarrow$ N between pure dimensional complex spaces has the local lifting property for cycles. From this result we also deduce that, under these hypotheses, several properties of M are transferred to N.