A Seifert algorithm for lamination links

TL;DR

This paper extends Seifert's algorithm to a broader class of lamination links, enabling the analysis of Seifert laminations in complex 3-manifold settings with framed measured lamination links.

Contribution

It introduces a generalized Seifert algorithm applicable to framed oriented measured lamination links in 3-manifolds.

Findings

Characterizes the set of framed lamination links bounding Seifert laminations

Analyzes the relationship between framings and Seifert surfaces in lamination links

Provides a framework for studying lamination links in fibered neighborhoods

Abstract

We generalize H. Seifert's algorithm for finding a Seifert surface for a knot or link. The generalization applies to "framed oriented measured lamination links." For knots, a Seifert surface determines a unique framing. In our setting, we analyze the set of framed lamination links which bound Seifert laminations and are carried by an $S^1$-fibered tube neighborhood of an oriented train track embedded in a 3-manifold.