Complexity of surgery manifolds and Cheeger-Gromov invariants

TL;DR

This paper establishes new lower bounds on the complexity of 3-manifolds obtained by Dehn surgery on knots, utilizing Cheeger-Gromov invariants, and provides explicit examples illustrating large gaps between Gromov norm and complexity.

Contribution

It introduces novel lower bounds on manifold complexity using Cheeger-Gromov rho invariants and constructs explicit hyperbolic 3-manifolds with significant complexity gaps.

Findings

New lower bounds on Dehn surgery manifold complexity

Explicit examples of hyperbolic 3-manifolds with large complexity gaps

Demonstration of the relationship between Gromov norm and manifold complexity

Abstract

We present new lower bounds on the complexity of Dehn surgery manifolds of knots, using our recent result on the Cheeger-Gromov rho invariants and triangulations. As an application, we give explicit examples of closed hyperbolic 3-manifolds with fixed first homology for which the gap between the Gromov norm and the complexity is arbitrarily large.