Partial immersions and partially free maps

Details Partial immersions and partially free maps Partial immersions and partially free maps

2010-10-26

arxiv.org/abs/1010.5362v1

Mathematics

Differential Geometry

8 pages, submitted to the proceedings of the conference DGA2010

Scientific paper

In a recent paper~\cite{DDL10} we studied basic properties of partial immersions and partially free maps, a generalization of free maps introduced first by Gromov in~\cite{Gro70}. In this short note we show how to build partially free maps out of partial immersions and use this fact to prove that the partially free maps in critical dimension introduced in Theorems 1.1-1.3 of~\cite{DDL10} for three important types of distributions can actually be built out of partial immersions. Finally, we show that the canonical contact structure on $\bR^{2n+1}$ admits partial immersions in critical dimension for every $n$.

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