An invariant of smooth 4–manifolds

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

Mathematical Subject Classification

Primary: 57R10

Secondary: 57N13

References

Forward citations

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

Volume 1, issue 1 (1997)

Laurence R Taylor