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Abstract
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We study the relationship between exotic
’s
and Stein surfaces as it applies to smoothing theory on more general open
–manifolds.
In particular, we construct the first known examples of large exotic
’s
that embed in Stein surfaces. This relies on an extension of
Casson’s embedding theorem for locating Casson handles in closed
–manifolds.
Under sufficiently nice conditions, we show that using these
’s as
end-summands produces uncountably many diffeomorphism types while
maintaining independent control over the genus-rank function and the Taylor
invariant.
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Keywords
exotic smooth structures, open $4$–manifolds, Stein
surfaces
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Mathematical Subject Classification 2010
Primary: 57N13
Secondary: 57R55
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Publication
Received: 25 November 2014
Revised: 20 September 2015
Accepted: 29 September 2015
Published: 1 July 2016
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