I am reading about Wirtinger presentations for knot groups but I am confused about how the Wirtinger presentation is preserved by the Reideimester moves. More specifically, I'm looking into a simple example, namely proving that $\langle x,y\rangle$ and $\langle x,y,z\mid z=xyx^{-1}\rangle$ are isomorphic which I get from applying a Type 2 Reideimester move to two trivial knots. I'm probably just really rusty on my group theory but I would appreciate any help!
2026-03-29 03:35:27.1774755327
Proving a quotient of a free group is also a free group - Wirtinger presentation
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