# Questions tagged [alexander-polynomial]

The alexander-polynomial tag has no usage guidance.

7
questions

**6**

votes

**0**answers

114 views

### 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**

vote

**0**answers

46 views

### 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**

votes

**1**answer

394 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**

votes

**0**answers

74 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**

votes

**1**answer

433 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**

votes

**1**answer

178 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**

votes

**3**answers

261 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 $\...