# Questions tagged [knot-link]

The knot-link tag has no usage guidance.

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### Flat or linkless embeddings of graph with fixed projection

The problem of finding whether a given planar diagram of a graph, with over- and under-crossings, is a linkless embedding or not has unknown complexity (Kawarabayashi et al., 2010). My first question ...

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**1**answer

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### Reference request: Can iterated torus links be mutated?

I believe that most iterated torus links cannot be changed non-trivially by a Conway mutation, as follows. If you look at the JSJ decomposition of the double-branched cover, then each satellite torus ...

**3**

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### Links defined by link-severance tableau

Consider a finite $n$-element classical (real) link and the resulting link structure obtained by cutting each of the component elements (knots). Let us represent the resulting structures in a tableau,...

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**2**answers

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### Tangled random triangles: One giant component?

Suppose you have $n$ triangles whose corners are random points on a sphere $S$
in $\mathbb{R}^3$.
Viewing the triangles as built from rigid bars as edges,
two triangles are linked if they cannot be ...

**3**

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134 views

### Infinitely many Brunnian links with bounded crossings

A set of Brunnian link is a nontrivial link such that if one component is removed, it becomes trivial. The best known example is the Borromean rings:
Here's a six component example:
There is likely ...

**0**

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**1**answer

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### Homogeneous links and crossings smoothing

Let $L$ be an oriented homogeneous link and let $D$ be an oriented diagram of $L$ wich is not necessarily a homogeneous diagram. Fix some crossing $c$ in $D$ and construct the diagram $D_0$ by ...

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**1**answer

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### Are all Torus Links in fact Lorenz links or not?

I'm currently trying to work through the material on Lorenz knots in the literature and there seems to be conflicting information.
On p. 66, in the Birman-Williams' paper Knotted Periodic Orbits in ...

**2**

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**1**answer

135 views

### Regular projection of a link, proof in the smooth category

Given two $C^1$ immersed curves $f, g: S^1 \to {\mathbb R}^3$ with disjoint image, I would like a simple proof, working only in the smooth category, that there exists a unit direction $y \in {\mathbb ...

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### Compare two topologies: Three 2-tori inside $S^3 \times S^1 \# S^2 \times S^2$ glued from two different diffeomorphisms

We like to ask for the comparison of two topologies of three 2-tori inside the same 4-manifolds glued from two different diffeomorphisms (see the end).
Given an embedded torus $T$ with trivial normal ...

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363 views

### Random rings linked into one component?

Let $S$ be a sphere of unit radius.
Let $C_n$ be a collection of unit-radius circles/rings whose centers
are (uniformly distributed)
random points in $S$, and which are oriented (tilted) randomly (...