✦ LIBER ✦
Maps of manifolds into the plane which lift to standard embeddings in codimension two
✍ Scribed by V.L. Carrara; M.A.S. Ruas; O. Saeki
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 265 KB
- Volume
- 110
- Category
- Article
- ISSN
- 0166-8641
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✦ Synopsis
Let f : M → R 2 be a smooth map of a closed n-dimensional manifold (n 2) into the plane and let π n+2 2 : R n+2 → R 2 be an orthogonal projection. We say that f has the standard lifting property, if every embedding f : M → R n+2 with π n+2 2 • f = f is standard in a certain sense. In this paper we give some sufficient conditions for a generic smooth map f to have the standard lifting property when M is a closed surface or an n-dimensional homotopy sphere.