#### Volume 15, issue 2 (2011)

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Directed immersions of closed manifolds

Geometry & Topology 15 (2011) 699–705
##### Abstract

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.

##### Keywords
Gauss map, spherical image, directed immersion, convex integration, h-principle, closed hypersurface, parallelizable manifold
##### Mathematical Subject Classification 2010
Primary: 53A07, 53C42
Secondary: 57R42, 58K15