Enhanced bounds for rho-invariants for both general and spherical 3-manifolds

Abstract

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.