#### Volume 1, issue 1 (1997)

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An invariant of smooth 4–manifolds

### Laurence R Taylor

Geometry & Topology 1 (1997) 71–89
 arXiv: math.GT/9712292
##### Abstract

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.

##### Keywords
smooth 4–manifolds, Stein manifolds, covering spaces
Primary: 57R10
Secondary: 57N13
##### Publication
Received: 21 October 1997
Accepted: 24 November 1997
Published: 6 December 1997
Proposed: Robion Kirby
Seconded: Ronald Stern, Ronald Fintushel
##### Authors
 Laurence R Taylor Department of Mathematics University of Notre Dame Notre Dame Indiana 46556 USA