Regular Maps on Euclidean Spaces and Tori
Shiquan Ren

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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Advanced Topics in Algebra
