Minimal genus in circle bundles over 3-manifolds

TL;DR

This paper establishes an estimate for the minimal genus of surfaces in circle bundles over irreducible 3-manifolds, linking it to self-intersection and Thurston norm, often achieving equality.

Contribution

It provides a new estimate for the genus function in circle bundles over 3-manifolds, clarifying its relation to topological invariants.

Findings

The estimate often equals the actual minimal genus.

The minimal genus relates to self-intersection and Thurston norm.

The result applies to irreducible 3-manifolds.

Abstract

An estimate for the genus function in circle bundles over irreducible 3-manifolds is proven. This estimate is in many cases an equality and it relates the minimal genus of the surfaces representing a given homology class with the self-intersection of the class and the Thurston norm of the underlying 3-manifold.