In this paper, we develop a geometric procedure for producing a “reverse” to Quillen’s plus construction, a construction called a -sided -cobordism or semi--cobordism. We then use this reverse to the plus construction to produce uncountably many distinct ends of manifolds called pseudocollars, which are stackings of -sided -cobordisms. Each of our pseudocollars has the same boundary and prohomology systems at infinity and similar group-theoretic properties for their profundamental group systems at infinity. In particular, the kernel group of each group extension for each -sided -cobordism in the pseudocollars is the same group. Nevertheless, the profundamental 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 .
The notion of pseudocollars originated in Hilbert cube manifold theory, where it was part of a necessary and sufficient condition for placing a -set as the boundary of an open Hilbert cube manifold.
"A Geometric Reverse to the Plus Construction and Some Examples of Pseudocollars on High-Dimensional Manifolds." Michigan Math. J. 67 (3) 485 - 509, August 2018. https://doi.org/10.1307/mmj/1522980163