  In this paper, we recall Quillen's plus construction for high-dimensional
smooth manifolds and the solution to the group extension problem. We then
develop a geometric procedure due for producing a "reverse" to the plus
construction, a one-sided s-cobordism called a semi-s-cobordism, when the total
group of the group extension is a semi-direct product. We then use this reverse
to the plus construction to produce uncountably many different one-ended
manifolds called pseudo-collars, which are stackings of semi-s- cobordisms. We
finally display a technique for producing "nice" one-ended open manifolds which
satisfy two of the necessary and suffcient conditions for being
pseudo-collarable but not the third.
