  In this paper, we develop a geometric procedure for producing a reverse to
Quillen's plus construction, a construction called a 1-sided h-cobordism or
semi-h-cobordism. We then use this reverse to the plus construction to produce
uncountably many distinct ends of manifolds called pseudo-collars, which are
stackings of 1-sided h-cobordisms. Each of our pseudo-collars has the same
boundary and pro-homology systems at infinity and similar group-theoretic
properties for their pro-fundamental group systems at infinity. In particular,
the kernel group of each group extension for each 1-sided h-cobordism in the
pseudo-collars is the same group. Nevertheless, the pro-fundamental group
systems at infinity are all distinct. A good deal of combinatorial group theory
is needed to verify this fact, including an application of Thompson's group V.
  The notion of pseudo-collars originated in Hilbert cube manfold theory, where
it was part of a necessary and suffcient condition for placing a Z-set as the
boundary of an open Hilbert cube manifold. We are interested in pseudo-collars
on finite-dimensional manifolds for the same reason, attempting to put a Z-set
as the boundary of an open high-dimensional manifold.
