一般三维流形和球面三维流形的rho-不变量的增强界
Enhanced bounds for rho-invariants for both general and spherical 3-manifolds
摘要：
我们建立了一般3-流形的Cheeger-Gromov rho-不变量的增强的界和特殊类3-流形的更强的界。作为关键成分，我们构造链零同伦的复杂性是线性有界的边界。这个结果可以看作是Gromov关于定量拓扑的猜想的一个代数拓扑类比。作者希望应用到各个领域，包括光滑结和谐群，定量拓扑学和复杂性理论。
英文摘要：
We establish enhanced bounds on Cheeger-Gromov rho-invariants for general 3-manifolds and yet stronger bounds for special classes of 3-manifold. As key ingredients, we construct chain null-homotopies whose complexity is linearly bounded by its boundary's. This result can be regarded as an algebraic topological analogue of Gromov's conjecture for quantitative topology. The author hopes for applications to various fields including the smooth knot concordance group, quantitative topology, and complexity theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
