The Complicated Twist and Pass Relation

I’m writing a little article about braid groups and loop braiding and I needed a picture of the following relation:

\[ \tau_{i+1}\rho_i = \sigma_i^{-1} \rho_i^{-1} \sigma_i \tau_i \]

It turns out that this diagram is incorrect! The twist $\tau_{i+1}$ is in the wrong direction. See [Complicated Relation Follow-Up](https://pgadey.ca/blog/complicated-relation-follow-up/) for a physical example.

The notation is that of:

Brendle, Tara E., and Allen Hatcher. “Configuration spaces of rings and wickets.” Commentarii Mathematici Helvetici 88.1 (2013): 131-162.

The paper is available here: https://pi.math.cornell.edu/~%20hatcher/Papers/wickets.pdf

The Complicated Twist and Pass Relation

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