Regular Maps on Cartesian Products and Disjoint Unions of Manifolds

Shiquan Ren

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arXiv · 1511.01601

Regular Maps on Cartesian Products and Disjoint Unions of Manifolds

Shiquan Ren

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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 in- dependent. For k-regular maps on manifolds, lower bounds of the dimension of the ambient Euclidean space have been exten- sively studied. In this paper, we study the lower bounds of the dimension of the ambient Euclidean space for 2-regular maps on Cartesian products of manifolds. As corollaries, we obtain the exact lower bounds of the dimension of the ambient Euclidean space for 2-regular maps and 3-regular maps on spheres as well as on some real projective spaces. Moreover, generalizing the notion of k-regular maps, we study the lower bounds of the di- mension of the ambient Euclidean space for maps with certain non-degeneracy conditions from disjoint unions of manifolds into Euclidean spaces.

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Shiquan Ren. 2015-11-05. Regular Maps on Cartesian Products and Disjoint Unions of Manifolds. https://arxiv.org/abs/1511.01601

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