Directed immersions of closed manifolds

Ghomi, Mohammad¹

¹ School of Mathematics, Georgia Institute of Technology, Atlanta GA 30332, USA

Geometry & topology, Tome 15 (2011) no. 2, pp. 699-705.

Résumé

Given any finite subset $X$ of the sphere $S^n$, $n\ge 2$, which includes no pairs of antipodal points, we explicitly construct smoothly immersed closed orientable hypersurfaces in Euclidean space $R^{n+1}$ whose Gauss map misses $X$. In particular, this answers a question of M Gromov.

Détail

DOI : 10.2140/gt.2011.15.699

Classification : 53A07, 53C42, 57R42, 58K15
Keywords: Gauss map, spherical image, directed immersion, convex integration, h-principle, closed hypersurface, parallelizable manifold

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