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

GT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to