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An invariant of smooth 4–manifolds

Laurence R Taylor

Geometry & Topology 1 (1997) 71–89

DOI: 10.2140/gt.1997.1.71

arXiv: math.GT/9712292

Abstract

We define a diffeomorphism invariant of smooth 4–manifolds which we can estimate for many smoothings of R4 and other smooth 4–manifolds. Using this invariant we can show that uncountably many smoothings of R4 support no Stein structure. Gompf constructed uncountably many smoothings of R4 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