## Geometry & Topology

### Exotic open $4$–manifolds which are nonleaves

#### Abstract

We study the possibility of realizing exotic smooth structures on finitely punctured simply connected closed $4$–manifolds as leaves of a codimension-one foliation on a compact manifold. In particular, we show the existence of uncountably many smooth open $4$–manifolds which are not diffeomorphic to any leaf of a codimension-one $C2$ foliation on a compact manifold. These examples include some exotic $ℝ4$’s and exotic cylinders $S3×ℝ$.

#### Article information

Source
Geom. Topol., Volume 22, Number 5 (2018), 2791-2816.

Dates
Revised: 13 November 2017
Accepted: 25 February 2018
First available in Project Euclid: 26 March 2019

https://projecteuclid.org/euclid.gt/1553565672

Digital Object Identifier
doi:10.2140/gt.2018.22.2791

Mathematical Reviews number (MathSciNet)
MR3811771

Zentralblatt MATH identifier
1397.37024

#### Citation

Meniño Cotón, Carlos; Schweitzer, Paul A. Exotic open $4$–manifolds which are nonleaves. Geom. Topol. 22 (2018), no. 5, 2791--2816. doi:10.2140/gt.2018.22.2791. https://projecteuclid.org/euclid.gt/1553565672

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