%0 Journal Article %T An invariant of smooth 4-manifolds %A Laurence R. Taylor %J Mathematics %D 1997 %I arXiv %R 10.2140/gt.1997.1.71 %X 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. %U http://arxiv.org/abs/math/9712292v1