Positive braid closures and taut foliations

TL;DR

This paper investigates the existence of taut foliations in the complements of positive braid closures in $S^3$, showing that certain Dehn surgeries produce non-L-spaces with taut foliations, extending understanding of 3-manifold topology.

Contribution

It establishes conditions under which Dehn surgeries on positive braid closures yield non-L-spaces with taut foliations, linking braid properties to 3-manifold foliation structures.

Findings

Dehn surgeries with slopes less than twice the genus minus one produce non-L-spaces.

Positive braid closures with non-unknot components admit taut foliations after specific surgeries.

Certain surgeries on positive braid closures do not produce L-spaces, indicating rich foliation structures.

Abstract

We study taut foliations on the complements of non-split positive braid closures in $S^3$. If $L$ is such a link with components $L_1,\ldots,L_n$ and at least one component is not the unknot, then the Dehn surgery along a multislope $(s_1,\ldots,s_n)\in\mathbb{Q}^n$ satisfying $s_i<2g(L_i)-1$ for $i=1,2,\ldots, n$ yields a non-L-space that admits a co-oriented taut foliation.