# Questions tagged [alexander-polynomial]

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7
questions

**6**

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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 ...

**1**

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**0**answers

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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 ...

**8**

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**1**answer

388 views

### Are there knots that can be distinguished by the Alexander-Conway polynomial, but not the Alexander polynomial?

On page 9 of Kauffman's Formal Knot theory, Kauffman claims
The Alexander-Conway Polynomial is a true refinement of the Alexander Polynomial. Because it is defined absolutely (rather than up to ...

**2**

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73 views

### 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 ...

**6**

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**1**answer

426 views

### HOMFLYPT vs. Jones vs. Alexander polynomial?

I'm searching for examples (perhaps the simplest one?) to show that the HOMFLYPT polynomial is stronger than the Jones and Alexander polynomial, respectively.
Any ideas what is the 1st knot in the ...

**3**

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**1**answer

162 views

### Multivariate Alexander polynomial vs single variable (Conway) Alexander polynomial

I consider the multivariate Alexander polynomial $\Delta(t_1,\ldots,t_n)$ for a $n$-component link (defined using e.g. the Fox derivative).
If we wish to construct a 1-variable polynomial $A(t)$, we ...

**2**

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**3**answers

250 views

### Multivariable vs single variable Alexander polynomial for links?

If we take a $n$-component link $L$, we have the multivariable Alexander polynomial $\Delta(L)(t_1,\ldots,t_n)$. Is there a standard single-variable Alexander polynomial? If yes, is it just euqal to $\...