关于高维流形上伪领结构的若干结果
Some Results on Pseudo-Collar Structures on High-Dimensional Manifolds
摘要：
本文回顾了Quillen关于高维光滑流形的加法构造和群扩张问题的求解。然后，我们开发了一个几何过程，由于生产“反向”的加建设，一个片面的s-协边称为半s-协边，当总群的群扩展是一个半直积。然后，我们使用这个逆的加号结构来产生无数个不同的单端流形，称为伪领，这是半s-协边的堆叠。最后，我们展示了一种技术，用于生产“漂亮”的一端开放的流形，满足两个必要和充分的条件是pseudo-collarable，但不是第三。
英文摘要：
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.
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