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      Questions tagged [knot-link]

      The tag has no usage guidance.

      8
      votes
      1answer
      257 views

      Does there exist a discrete gauge theory as a TQFT detecting the figure-8 knot?

      My question: Does there exist a discrete gauge theory as TQFT detecting the figure-8 knot? By detecting, I mean that computing the path integral (partition function with insertions of the knot/...
      2
      votes
      0answers
      28 views

      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 ...
      6
      votes
      1answer
      146 views

      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
      votes
      1answer
      131 views

      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,...
      10
      votes
      2answers
      312 views

      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
      votes
      1answer
      137 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
      votes
      1answer
      53 views

      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 ...
      2
      votes
      1answer
      112 views

      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
      votes
      1answer
      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 ...
      2
      votes
      0answers
      87 views

      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 ...
      17
      votes
      2answers
      364 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 (...

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