Symmetric Whitney tower cobordism for bordered 3-manifolds and links

TL;DR

This paper develops a new framework for studying cobordism between bordered 3-manifolds using symmetric Whitney towers, introducing obstructions based on Cheeger-Gromov rho-invariants, with applications to link concordance.

Contribution

It introduces symmetric Whitney tower cobordism for bordered 3-manifolds and provides new obstructions using amenable Cheeger-Gromov rho-invariants, extending previous results.

Findings

Obstructions to cobordism via rho-invariants

Application to link exteriors and nonzero linking number links

Revealed new structures in link concordance

Abstract

We introduce a notion of symmetric Whitney tower cobordism between bordered 3-manifolds, aiming at the study of homology cobordism and link concordance. It is motivated by the symmetric Whitney tower approach to slicing knots and links initiated by Cochran, Orr, and Teichner. We give amenable Cheeger-Gromov rho-invariant obstructions to bordered 3-manifolds being Whitney tower cobordant. Our obstruction is related to and generalizes several prior known results, and also gives new interesting cases. As an application, our method applied to link exteriors reveals new structures on (Whitney tower and grope) concordance between links with nonzero linking number, including the Hopf link.