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We establish enhanced bounds on Cheeger-Gromov rho-invariants for general3-manifolds and yet stronger bounds for special classes of 3-manifold. As keyingredients, we construct chain null-homotopies whose complexity is linearlybounded by its boundary's. This result can be regarded as an algebraictopological analogue of Gromov's conjecture for quantitative topology. Theauthor hopes for applications to various fields including the smooth knotconcordance group, quantitative topology, and complexity theory.

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