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Topology

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Difficult

Trefoil Knot

TOPO-YCEZGX

Let $K\subset\mathbb R^3$ be a trefoil knot.

Which of the following is a valid presentation of $\pi_1(\mathbb R^3-K)$?

A

$\langle a,b\mid ab=ba\rangle$

B

$\langle a,b\mid aba=bab\rangle$

C

$\langle a,b\mid aba^{-1}=bab^{-1}\rangle$

D

$\langle a,b\mid aba^{-1}ba=bab^{-1}ab\rangle$

E

$\langle a,b\mid ababa=babab\rangle$