#### Geometry & Topology, Vol. 1 (1997)
Paper no. 6, pages 71-89.

## An invariant of smooth 4-manifolds

### Laurence R Taylor

**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 has 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

**AMS subject classification**.
Primary: 57R10.
Secondary: 57N13.

**DOI:** 10.2140/gt.1997.1.71

**E-print:** `arXiv:math.GT/9712292`

Submitted to GT on October 21, 1997.
Paper accepted November 24, 1997.

Notes on file formats
Laurence R Taylor

Department of Mathematics

University of Notre Dame

Notre Dame, IN 46556

USA

Email: taylor.2@nd.edu

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