Geometry & Topology 15 (2011) 699–705

DOI: 10.2140/gt.2011.15.699

Abstract

Given any finite subset X of the sphere Sⁿ, n ≥ 2, which includes no pairs of antipodal points, we explicitly construct smoothly immersed closed orientable hypersurfaces in Euclidean space Rⁿ⁺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

Primary: 53A07, 53C42

Secondary: 57R42, 58K15

References

Publication

Received: 25 October 2010
Accepted: 13 March 2011
Published: 9 May 2011
Proposed: Yasha Eliashberg
Seconded: Leonid Polterovich, Dmitri Burago

Authors