An invariant of smooth 4-manifolds

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.

19 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol1/paper6.abs.html

References in corpus (2)

• Handlebody Construction of Stein Surfaces
• Smooth structures on collarable ends of 4-manifolds

Cited by in corpus (11)

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• ASD moduli spaces over four-manifolds with tree-like ends
• Group actions, corks and exotic smoothings of R^4
• Creating Stein surfaces by topological isotopy
• Exotic open $4$-manifolds which are non-leaves
• Topologically trivial proper 2-knots
• Exotic non-leaves with infinitely many ends