A combinatorial move on the set of Jenkins-Strebel differentials

TL;DR

This paper introduces a simple combinatorial move on Jenkins-Strebel differentials with a single horizontal cylinder, supported by computational evidence suggesting a correspondence with connected strata components.

Contribution

It proposes a new combinatorial move on quadratic differentials and provides computational evidence linking these moves to the topology of strata components.

Findings

The combinatorial move is elementary and well-defined.

Computer experiments indicate a one-to-one correspondence with connected strata components.

Supports a conjecture relating combinatorial classes to topological strata.

Abstract

We describe an elementary combinatorial move on the set of quadratic differentials with a horizontal one cylinder decom-position. Computer experiment suggests that the corresponding equivalent classes are in one-to-one correspondence with the con-nected component of the strata.