(-2,3,7)-pretzel knot and Reebless foliation

TL;DR

This paper investigates the conditions under which Dehn surgeries on the (-2,3,7)-pretzel knot yield 3-manifolds that lack Reebless foliations, identifying specific parameter constraints.

Contribution

It establishes new criteria for the absence of Reebless foliations in 3-manifolds obtained from Dehn surgeries on the (-2,3,7)-pretzel knot.

Findings

Dehn surgery with p/q > 18 and p odd produces no Reebless foliation

The case p/q = 37/2 is an exception

Specific parameter ranges determine the foliation properties

Abstract

If p/q > 18, p is odd, and $p/q \ne 37/2$, (p,q)-Dehn surgery for the (-2,3,7)-pretzel knot produces a 3-manifold without Reebless foliation.