Questions tagged [alexander-polynomial]
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Why does the inverse Alexander polynomial appear in the MMR conjecture?
In an attempt to better understand why the inverse Alexander polynomial appears in the MMR conjecture, I was reading the paper [1] of Bar-Natan and Garoufalidis giving their proof of the conjecture ...
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General formula for a topologically slice odd pretzel knot
An odd 3-strand pretzel knot $K=P(p,q,r)$ has $\Delta_K(t)=1$ if $pq+pr+qr=1$. This fact, along with a theorem of Fintushel and Stern (every odd 3-pretzel knot with trivial Alexander polynomial is not ...
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Is there a measure of the failure of the Alexander polynomial to distinguish knots?
Has there been any research into something like the ratio of distinct Alexander-indistinguishable knots to total knots (up to some measure of complexity)? This was a random question asked of me by a ...
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Undirected Alexander polynomial (sort of)
Take the skein relation of the Alexander polynomial: $S^1-S^{-1}-zS^0=0$, where z is the parameter of the Alexander polynomial and $S$ the overcross braid element. "Multiply" the equation with ...
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