Geometry & Topology

Exotic open $4$–manifolds which are nonleaves

Carlos Meniño Cotón and Paul A Schweitzer

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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 4’s and exotic cylinders S3×.

Article information

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

Received: 25 November 2016
Revised: 13 November 2017
Accepted: 25 February 2018
First available in Project Euclid: 26 March 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37C85: Dynamics of group actions other than Z and R, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx] 53C12: Foliations (differential geometric aspects) [See also 57R30, 57R32] 57R30: Foliations; geometric theory
Secondary: 57R55: Differentiable structures

exotic $\mathbb{R}^4$ nonleaves codimension-one foliations


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.

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