论文标题
$ n $二维的klein瓶及其理性betti数字
Real Bott manifold structure of $n$-dimensional Klein bottle and its rational Betti numbers
论文作者
论文摘要
唐纳德·戴维斯（Donald Davis）开始了对克莱因瓶的$ n $维度类似物的研究。这个广义的klein瓶是作为平面多边形的模量空间而出现的，用于一定的侧面长度。在本文中，我们表明$ n $维的klein瓶是一个真正的bott歧管，并确定相应的bott矩阵。我们确定了其他两类平面多边形的模量空间上的小盖结构。作为应用程序，由于Suciu和Trevisan，我们使用公式来计算这些空间的合理betti数字。
Donald Davis initiated the study of an $n$-dimensional analogue of the Klein bottle. This generalized Klein bottle occurs as a moduli space of planar polygons for a certain choice of side lengths. In this paper, we show that the $n$-dimensional Klein bottle is a real Bott manifold and determine the corresponding Bott matrix. We determine the small cover structure on two other classes of moduli spaces of planar polygons. As an application, we compute the rational Betti numbers of these spaces using a formula, due to Suciu and Trevisan.
