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What you want is Alexander s Theorem which describes explicitly how to convert every knot or link into a closed braid The process is pretty simple Here is a nice description I ll say briefly
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
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One can also characterize the knot determinant as being the order of the first homology of the double branched cover which takes a lot less algebraic machinery Or the
While it is indeed very quick to do this with Alexander duality you can still do this with the Mayer Vietoris sequence and with a tiny bit of Poincare duality
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A framed knot can be imagined as a knot tied in a ribbon with width rather than a 1 dimensional string We also want the ribbon to link back up to itself exactly so you can
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https://math.stackexchange.com › questions
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
https://math.stackexchange.com › questions › understand-the-knot-grou…
I have the difficulty to understand the knot group of the 2 component link in mathbb R 3 especially it is not commutitive
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
I have the difficulty to understand the knot group of the 2 component link in mathbb R 3 especially it is not commutitive
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