For oriented manifolds of dimension at least
that
are simply connected at infinity, it is known that end summing is a uniquely defined
operation. Calcut and Haggerty showed that more complicated fundamental group
behavior at infinity can lead to nonuniqueness. We examine how and when
uniqueness fails. Examples are given, in the categories
top,
pland
diff, of
nonuniqueness that cannot be detected in a weaker category (including the homotopy
category). In contrast, uniqueness is proved for Mittag-Leffler ends, and
generalized to allow slides and cancellation of (possibly infinite) collections of
– and
–handles
at infinity. Various applications are presented, including an
analysis of how the monoid of smooth manifolds homeomorphic to
acts on the smoothings of
any noncompact
–manifold.
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