Geometry & Topology

Directed immersions of closed manifolds

Mohammad Ghomi

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Abstract

Given any finite subset X of the sphere Sn, n2, 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.

Article information

Source
Geom. Topol., Volume 15, Number 2 (2011), 699-705.

Dates
Received: 25 October 2010
Accepted: 13 March 2011
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732302

Digital Object Identifier
doi:10.2140/gt.2011.15.699

Mathematical Reviews number (MathSciNet)
MR2800363

Zentralblatt MATH identifier
1242.53006

Subjects
Primary: 53A07: Higher-dimensional and -codimensional surfaces in Euclidean n-space 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 57R42: Immersions 58K15: Topological properties of mappings

Keywords
Gauss map spherical image directed immersion convex integration h-principle closed hypersurface parallelizable manifold

Citation

Ghomi, Mohammad. Directed immersions of closed manifolds. Geom. Topol. 15 (2011), no. 2, 699--705. doi:10.2140/gt.2011.15.699. https://projecteuclid.org/euclid.gt/1513732302


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