Regular Maps on Euclidean Spaces and Tori

TL;DR

This paper investigates the minimal dimensions of Euclidean spaces needed for complex k-regular maps from Euclidean spaces, providing new lower bounds for such embeddings.

Contribution

It introduces new lower bounds on the ambient space dimension for complex k-regular maps on Euclidean spaces, advancing understanding of their geometric constraints.

Findings

Established lower bounds for complex k-regular maps

Extended previous results on regular map dimensions

Contributed to the theory of embeddings of manifolds

Abstract

A map from a manifold to a Euclidean space is said to be k-regular if the image of any distinct k points are linearly independent. In this paper, we give some lower bounds of the dimension of the ambient Euclidean space for complex k-regular maps on Euclidean spaces.