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

A Geometric Reverse To The Plus Construction And Some Examples Of Pseudo-Collars On High-Dimensional Manifolds