闭路空间的系统自由度
Systolic freedom of loop space
摘要：
给定一对整数m和n，使得1 < m < n，证明了每个n维流形都有任意小总体积的度量，并且具有如下性质：每个小于单位m-体积的m维子流形必同调挠.这一结果不同于一对互补维数的情形，对于互补维数，直接的尺规作图法起作用，并给出完全一般性的类似定理。在本文中，我们使用沙利文的望远镜模型的合理化空间观察收缩自由。
英文摘要：
Given a pair of integers m and n such that 1 < m < n, we show that every n-dimensional manifold admits metrics of arbitrarily small total volume, and possessing the following property: every m-dimensional submanifold of less than unit m-volume is necessarily torsion in homology. This result is different from the case of a pair of complementary dimensions, for which a direct geometric construction works and gives the analogous theorem in complete generality. In the present paper, we use Sullivan's telescope model for the rationalisation of a space to observe systolic freedom.
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