We study exotic smoothings of open
–manifolds using
the minimal-genus function and its analog for end homology. While traditional techniques in
open
–manifold
smoothing theory give no control of minimal genera, we make progress by
using the adjunction inequality for Stein surfaces. Smoothings can be
constructed with much more control of these genus functions than the
compact setting seems to allow. As an application, we expand the range of
–manifolds
known to have exotic smoothings (up to diffeomorphism). For example, every
–handlebody
interior (possibly infinite or nonorientable) has an exotic smoothing, and “most” have
infinitely many, or sometimes uncountably many, distinguished by the genus
function and admitting Stein structures when orientable. Manifolds with
–homology
are also accessible. We investigate topological submanifolds of smooth
–manifolds.
Every domain of holomorphy (Stein open subset) in
is
topologically isotopic to uncountably many other diffeomorphism types of domains of
holomorphy with the same genus functions, or with varying but controlled genus
functions.