## Geometry & Topology

### Directed immersions of closed manifolds

#### 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.

#### Article information

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

Dates
Accepted: 13 March 2011
First available in Project Euclid: 20 December 2017

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

#### 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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