An invariant of smooth 4–manifolds

Taylor, Laurence R¹

¹ Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, USA

Geometry & topology, Tome 1 (1997) no. 1, pp. 71-89.

Résumé

We define a diffeomorphism invariant of smooth 4–manifolds which we can estimate for many smoothings of ${ℝ}^4$ and other smooth 4–manifolds. Using this invariant we can show that uncountably many smoothings of ${ℝ}^4$ support no Stein structure. Gompf constructed uncountably many smoothings of ${ℝ}^4$ which do support Stein structures. Other applications of this invariant are given.

Détail

DOI : 10.2140/gt.1997.1.71

Keywords: smooth 4–manifolds, Stein manifolds, covering spaces

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