Directed immersions of closed manifolds

Details Directed immersions of closed manifolds Directed immersions of closed manifolds

2010-10-12

arxiv.org/abs/1010.2429v3

Mathematics

Differential Geometry

Minor revisions over the last draft

Scientific paper

Given any finite subset X of the sphere S^n, n>1, 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.

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