Some remarks on Thom's Transversality Theorem

TL;DR

This paper revisits Thom's Transversality Theorem through a Gromov-inspired perspective, avoiding Sard's Theorem and providing more detailed insights into the structure of non-transverse maps.

Contribution

It introduces a novel approach to Thom's Transversality Theorem that bypasses Sard's Theorem and yields finer structural information about non-transverse maps.

Findings

Avoids Sard's Theorem in the proof of Thom's Transversality Theorem

Provides detailed structural insights into non-transverse maps

Enhances understanding of transversality conditions

Abstract

We study Thom Transversality Theorem using a point of view, suggested by Gromov, which allows to avoid the use of Sard Theorem and gives finer informations on the structure of the set of non-transverse maps.