Immersibility of manifolds is decidable in odd codimension

TL;DR

This paper presents an algorithm that determines whether a smooth map between closed oriented manifolds of odd codimension can be homotoped to an immersion, addressing a fundamental question in differential topology.

Contribution

It introduces a decidability algorithm for immersibility of manifolds in odd codimension, advancing understanding of manifold immersion problems.

Findings

Decidability of immersibility in odd codimension established

Algorithmic approach for smooth maps between manifolds developed

Addresses a key problem in differential topology

Abstract

Given a smooth map $f:M\rightarrow N$ of closed oriented smooth manifolds, is there an immersion homotopic to $f$? We provide an algorithm that decides this when the codimension of the manifolds is odd.