All Questions
Tagged with knot-link knot-theory
10 questions with no upvoted or accepted answers
8
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Is the number of prime factors of 3-manifolds obtained by Dehn surgery along a link with $N$ components in $S^3$ bounded from above?
For a given $N$, is the number of prime factors of 3-manifolds obtained by Dehn surgery along a link with $N$ components in $S^3$ bounded from above?
The Two Summands Conjecture states that surgery ...
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7
votes
0
answers
130
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Generalized Brunnian links
A Brunnian link of order $n$ is nontrivial link of $n$ rings
that becomes a trivial link of $n-1$ rings if any ring is
removed. They were classified up to link-homotopy by
Milnor in 1954. This ...
- 50.8k
6
votes
0
answers
211
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$\mathbb{Z}/2\mathbb{Z}$ coefficients in gysin sequence
I am reading the article "Signature of links" by Kauffman and Taylor. Here they show that it is possible to calculate the nullity of a link $L\subset S^3$ by knowing the first betti number of the ...
- 521
5
votes
0
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328
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Are there examples of different knots with identical Jones polynomials and different Seifert Genus?
I had asked this question on math.stackexchange 2 days back but came up empty handed so I wanted to ask it here.
Are there known examples of $2$ non equivalent knots that have identical jones ...
- 2,689
4
votes
0
answers
112
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Coloured Jones polynomial of the mirror image of a multicomponent link
This question has been reposted from MathStackExchange
It is well understood that the usual Jones polynomial of a knot or link can be related to the Jones polynomial of the mirror image of the knot/...
- 81
2
votes
0
answers
44
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Link invariants on a thickened surface
Let $\Sigma$ be an oriented surface. I want to know about link invariants in $\Sigma\times [0,1]$. I already know the Ozawa polynomial introduced in this paper, but I couldn’t find any other than that....
- 21
2
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0
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80
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Composition of 3-braids to obtain braids with trivial closure
Given a 3-braid $b=\sigma_1\sigma_2^{-1}\sigma_1\sigma_2^{-1}\sigma_1$ (which has non-trivial closure), can we find a 3-braid $c$, which has trivial closure (closure results in any trivial knot or ...
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2
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0
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135
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Möbius cross energy in $S^3$?
Let $\gamma_i$, $i=1,2$ be two loops in $\mathbb R^3$. The Möbius cross energy of the pair is defined by
$$
E(\gamma_1, \gamma_2)=\iint_{S^1\times S^1}\frac{|\gamma'_1(u)|\cdot|\gamma'_2(v)|}{|\...
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0
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181
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How does the extra rope length of this link/tangle scale with the inner triangle size?
The symmetric chiral link made of three long intertwined/linked/tangled flexible ropes of radius 1 shown in the figure, whose 6 ends all lie in a plane at spatial infinity and which are pulled ...
- 9
0
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Is the 3d writhe of ideal knots proportional to their smallest possible 2d writhe?
In a knot, the (two-dimensional) or 2d writhe is the sum of all positive crossings minus the sum of all negative crossings. The 2d writhe is always an integer. There is also, for each knot, a smallest ...
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