Exotic open 4–manifolds which are nonleaves

Meniño Cotón, Carlos¹ ; Schweitzer, Paul²

¹ Departamento de Análise, Instituto de Matemática e Estatística, Universidade Federal Fluminense, Niterói, Rio de Janeiro-RJ, Brazil
² Departamento de Matemática, Pontificia Universidade Católica do Rio de Janeiro, Gávea, Rio de Janeiro-RJ, Brazil

Geometry & topology, Tome 22 (2018) no. 5, pp. 2791-2816.

Résumé

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 $S^3\times ℝ$.

Détail

DOI : 10.2140/gt.2018.22.2791

Classification : 37C85, 53C12, 57R30, 57R55
Keywords: exotic $\mathbb{R}^4$, nonleaves, codimension-one foliations

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