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 for a physical example.
The notation is from the following paper.
Brendle, Tara E., and Allen Hatcher. “Configuration spaces of rings and wickets.” Commentarii Mathematici Helvetici 88.1 (2013): 131-162.
Published: Oct 8, 2024 @ 09:40.
Last Modified: Oct 17, 2026 @ 07:19.
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