Problems around 3-manifolds

TL;DR

This paper discusses various open problems in 3-manifold topology, including minimal surfaces, Ricci flow, and Heegaard splittings, reflecting on recent developments and unresolved issues in the field.

Contribution

It provides a personal perspective on key open problems in 3-manifold topology, highlighting areas influenced by recent breakthroughs like the Hamilton-Perelman revolution.

Findings

Identifies unresolved issues in minimal surfaces and Ricci flow.

Highlights challenges in understanding Haken 4-manifolds and contact structures.

Discusses the impact of recent advances on classical problems.

Abstract

This is a personal view of some problems on minimal surfaces, Ricci flow, polyhedral geometric structures, Haken 4-manifolds, contact structures and Heegaard splittings, singular incompressible surfaces after the Hamilton-Perelman revolution.