论文标题
定量拓扑的迭代积分
Iterated Integrals in Quantitative Topology
论文作者
论文摘要
令X为简单连接的Riemannian歧管。到目前为止，定量拓扑已将沙利文的理性同义理论用作X上的几何信息与无扭转同型理论信息之间的桥梁。在本文中，我们在这两个区域之间引入了Chen在X的基于X的循环空间上的迭代积分作为新的桥梁。我们给出了两种应用：在X上寻找Gromov较高同型基团的上限，并证明在最多L长度为X的环路上，在X的X上，在X的X上，在X的空间中不存在同源性非平凡的小体积周期。
Let X be a simply connected Riemannian manifold. Until now, quantitative topology has used Sullivan's rational homotopy theory as the bridge between geometric information on X and torsion-free homotopy theoretic information on X. In this paper we introduce Chen's iterated integrals on the based loop space of X as a new bridge between these two areas. We give two applications: finding upper bounds for Gromov's distortion of higher homotopy groups on X and also proving the non-existence of homologically non-trivial small-volume cycles in the space of loops on X of length at most L.
