Volume 15, issue 2 (2011)

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Directed immersions of closed manifolds

Mohammad Ghomi

Geometry & Topology 15 (2011) 699–705
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 2010
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
Mohammad Ghomi
School of Mathematics
Georgia Institute of Technology
Atlanta GA 30332
USA
http://www.math.gatech.edu/~ghomi