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

TL;DR

This paper improves bounds on Cheeger-Gromov rho-invariants for 3-manifolds, providing stronger results for specific classes and introducing chain null-homotopies with linearly bounded complexity, with potential applications across multiple fields.

Contribution

It establishes enhanced bounds on rho-invariants and constructs chain null-homotopies with linear complexity bounds, advancing quantitative topology and related areas.

Findings

Stronger bounds for rho-invariants on special 3-manifolds

Construction of chain null-homotopies with linear boundary complexity

Potential applications to knot concordance and complexity theory

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.