Subexponential groups in 4-manifold topology

TL;DR

This paper provides an elementary proof that certain topological techniques in 4-manifold topology are valid for manifolds with subexponential fundamental groups, including a correction and reformulation of growth estimates.

Contribution

It offers a simpler proof of the Freedman-Teichner result and refines growth estimates using coarse geometry, enhancing understanding of 4-manifold classification.

Findings

Proof of the validity of classification techniques for subexponential groups

Correction and clarification of growth estimates in the original proof

Reformulation of growth conditions in terms of coarse geometry

Abstract

We present a new, more elementary proof of the Freedman-Teichner result that the geometric classification techniques (surgery, s-cobordism, and pseudoisotopy) hold for topological 4-manifolds with groups of subexponential growth. In an appendix Freedman and Teichner give a correction to their original proof, and reformulate the growth estimates in terms of coarse geometry.