Extension theorems for analytic objects associated to foliations

TL;DR

This paper proves a structure theorem for extending analytic objects linked to one-dimensional foliation germs on surfaces across barriers, and applies it to extend projective transverse structures.

Contribution

It introduces a new structure theorem for extending analytic objects in foliation theory and applies it to projective transverse structures.

Findings

Extension theorem for analytic objects across barriers

Structure theorem for germs of foliations on surfaces

Application to projective transverse structures

Abstract

In this paper we will establish a structure theorem concerning the extension of analytic objects associated to germs of dimension one foliations on surfaces, through one-dimensional barriers. As an application, an extension theorem for projective transverse structures is obtained.