Explicitly describing fibered 3-manifolds through families of singularly fibered surfaces

TL;DR

This paper provides an explicit method to describe fibered 3-manifolds, specifically the complements of closures of homogeneous braids, by analyzing how fibers intersect cross-sections of the 3-sphere.

Contribution

It introduces a novel explicit description of fibered 3-manifolds using families of singularly fibered surfaces, enhancing understanding of their fiber structures.

Findings

Explicit description of fibered 3-manifolds

Analysis of fiber intersections with 3-sphere cross-sections

Application to complements of homogeneous braid closures

Abstract

We give an explicit description of a fibration of the complement of the closure of a homogeneous braid, understanding how each fiber intersects every cross-section of $S^3$.