Taut foliations, left-orderability, and cyclic branched covers

TL;DR

This paper investigates the conditions under which cyclic branched covers of knots possess taut foliations, have left-orderable fundamental groups, and are not L-spaces, linking topological properties with algebraic and geometric structures.

Contribution

It provides new criteria and insights into the relationship between taut foliations, left-orderability, and L-space properties in cyclic branched covers of knots.

Findings

Identifies conditions for cyclic branched covers to admit taut foliations.

Establishes links between left-orderability and topological features.

Shows when these covers are not L-spaces.

Abstract

We study the question of when cyclic branched covers of knots admit taut foliations, have left-orderable fundamental group, and are not L-spaces.