Exotic open 4–manifolds which are nonleaves

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 $C^{2}$ foliation on a compact manifold. These examples include some exotic $ℝ^{4}$ ’s and exotic cylinders $S^{3} \times ℝ$ .

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Keywords

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

Mathematical Subject Classification 2010

Primary: 37C85, 53C12, 57R30

Secondary: 57R55

References

Publication

Received: 25 November 2016

Revised: 13 November 2017

Accepted: 25 February 2018

Published: 1 June 2018

Proposed: Yasha Eliashberg

Seconded: András I Stipsicz, Leonid Polterovich

Authors

Carlos Meniño Cotón
Departamento de Análise, Instituto de Matemática e Estatística Universidade Federal Fluminense Niterói Rio de Janeiro-RJ Brazil

Paul A Schweitzer
Departamento de Matemática Pontificia Universidade Católica do Rio de Janeiro Gávea Rio de Janeiro-RJ Brazil

Volume 22, issue 5 (2018)

Carlos Meniño Cotón and Paul A Schweitzer

Abstract