# Questions tagged [knot-invariants]

For properties of knots that remain unaffected by Reidmaster moves

228 questions
Filter by
Sorted by
Tagged with
26 views

### Unusual skein relation in HOMFLY polynomial

If I take the HOMFLY(PT) polynomial defined by $$l \,P(L_+) + l^{-1}\,P(L_-) + m\,P(L_0) = 0,$$ I have looked at expressions of the form (knots that are the same except inside a small disk, where ...
50 views

### Given a sequence of head to tail vectors forming a closed loop, how can I determine if they form a knot? [closed]

Consider if we have some sequence of vectors placed head to tail which form a closed loop. How can one determine whether they form a loop? We assume that it is given that the vectors close, that is ...
38 views

69 views

### Computation of the A-polynomial of the trefoil knot

What is the A-polynomial of the trefoil knot? Show the steps. I would like to compute the A-polynomial of the trefoil knot, whose fundamental group is given by: $$\langle x, y | x^2 = y^3 \rangle$$ ...
26 views

61 views

### Prove that the equivalence of 2 knots is an equivalence relation.

The definition of equivalence of 2 knots according to Richard H. Crowell and Ralph H. Fox, edition 1963, is: Assume that $K_{1}$,$K_{2}$ are 2 knots in $\mathbb{R^3}$, then they are equivalent , ...
35 views

### Show that the number of tame knot types is at most countable.

Show that the number of tame knot types is at most countable. I want a hint for solving this problem please.
20 views

### The regions into which $\mathbb{R^2}$ is divided by regular projections can be colored into white and black.

Show that the regions into which $\mathbb{R^2}$ is divided by a regular projection can be colored white and black in such a way that adjacent regions are of opposite colors ( as on chessbord). Could ...
### Devise a method for constructing a table of knots, and use it to find $10$ knots of not more than $6$ crossings.
Devise a method for constructing a table of knots, and use it to find $10$ knots of not more than $6$ crossings (do not consider the question of whether these are really distinct types.) Could anyone ...