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Again, keeping with our 2-bridge knots, every two bridge knot has a knot group (another algebraic topology invariant) $\pi_1(S^3-K)$, has a presentation with two generators and one relation. Obviously, this is just how I look at knot theory, and I am sure you will get different opinions about it from other knot theorists, but I hope this might give a flavor for what it is we do.
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