Directed immersions of closed manifolds

Ghomi, Mohammad

doi:10.2140/gt.2011.15.699

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Directed immersions of closed manifolds

Mohammad Ghomi

Geometry & Topology 15 (2011) 699–705

DOI: 10.2140/gt.2011.15.699

Abstract

Given any finite subset $X$ of the sphere $S^{n}$ , $n \geq 2$ , 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

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

Volume 15, issue 2 (2011)