Boundary slopes of some non-Montesinos knots

TL;DR

This paper demonstrates that certain alternating non-Montesinos knots have essential spanning surfaces with extreme boundary slopes that are not represented by the standard checkerboard surfaces from their diagrams.

Contribution

It reveals that for some non-Montesinos knots, the extremal boundary slopes are not always realized by checkerboard surfaces, challenging previous assumptions.

Findings

Existence of alternating non-Montesinos knots with non-checkerboard extremal boundary slopes

Essential spanning surfaces with maximal and minimal boundary slopes differ from checkerboard surfaces

Provides new insights into the boundary slope spectrum of non-Montesinos knots

Abstract

It is shown that there exist alternating non-Montesinos knots whose essential spanning surfaces with maximal and minimal boundary slopes are not realised by the checkerboard surfaces coming from a reduced alternating planar diagram.