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

Yamamoto, Minoru

Illinois J. Math., Tome 51 (2007) no. 3, p. 705-721 / Harvested from Project Euclid

Résumé

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.

Publié le : 2007-07-15
Classification: 57R45, 57R40

@article{1258131098,
     author = {Yamamoto, Minoru},
     title = {Lifting a generic map of a surface into the plane to an embedding into 4-space},
     journal = {Illinois J. Math.},
     volume = {51},
     number = {3},
     year = {2007},
     pages = { 705-721},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258131098}
}

Yamamoto, Minoru. Lifting a generic map of a surface into the plane to an embedding into 4-space. Illinois J. Math., Tome 51 (2007) no. 3, pp.  705-721. http://gdmltest.u-ga.fr/item/1258131098/