Bounded cochains on 3-manifolds

TL;DR

This paper investigates the large-scale geometry of 3-manifolds with nontrivial 2-dimensional bounded cohomology to advance understanding related to the geometrization conjecture.

Contribution

It introduces new methods to analyze the geometry of 3-manifolds with bounded cohomology, aiming to prove a weak form of the geometrization conjecture.

Findings

Identifies conditions under which 3-manifolds have nontrivial bounded cohomology.

Establishes a connection between bounded cohomology and large-scale geometric properties.

Provides partial results supporting a weak geometrization conjecture.

Abstract

We study the large-scale geometry of 3-manifolds with nontrivial 2-dimensional bounded cohomology, with a view to proving a weak version of the geometrization conjecture for such manifolds.