Computing the Maximum Slope Invariant in Tubular Groups

TL;DR

This paper demonstrates that the maximum slope invariant in tubular groups can be computed easily and can distinguish groups beyond traditional methods like edge pattern analysis or isoperimetric functions.

Contribution

It introduces a straightforward method for calculating the maximum slope invariant and shows its effectiveness in differentiating tubular groups.

Findings

Maximum slope invariant is easy to compute.

Maximum slope can distinguish groups not separable by edge pattern or isoperimetric function.

Provides explicit examples of distinguishable tubular groups.

Abstract

We show that the maximum slope invariant for tubular groups is easy to calculate, and give an example of two tubular groups that are distinguishable by their maximum slopes but not by edge pattern considerations or isoperimetric function.