## Illinois Journal of Mathematics

### Lifting a generic map of a surface into the plane to an embedding into 4-space

Minoru Yamamoto

#### Abstract

Let $f:M \to \mathbf{R}^2$ be a stable map of a closed surface $M$ into the plane and $\pi^2_2:\mathbf{R}^4 \to \mathbf{R}^2$ the orthogonal projection. In this paper, we will show that for any such $f$ there exists an embedding $F:M \to \mathbf{R}^4$ such that $f=\pi^2_2 \circ F$ is satisfied.

#### Article information

Source
Illinois J. Math., Volume 51, Number 3 (2007), 705-721.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258131098

Digital Object Identifier
doi:10.1215/ijm/1258131098

Mathematical Reviews number (MathSciNet)
MR2379718

Zentralblatt MATH identifier
1154.57027

Subjects
Primary: 57R45: Singularities of differentiable mappings
Secondary: 57R40: Embeddings

#### Citation

Yamamoto, Minoru. Lifting a generic map of a surface into the plane to an embedding into 4-space. Illinois J. Math. 51 (2007), no. 3, 705--721. doi:10.1215/ijm/1258131098. https://projecteuclid.org/euclid.ijm/1258131098