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 4 and other smooth 4–manifolds. Using this invariant we can show that uncountably many smoothings of 4 support no Stein structure. Gompf constructed uncountably many smoothings of 4 which do support Stein structures. Other applications of this invariant are given.

Keywords
smooth 4–manifolds, Stein manifolds, covering spaces
Mathematical Subject Classification
Primary: 57R10
Secondary: 57N13
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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