Imagine that we have a (very) large shell full of holes, and flexible strings go (randomly) from one hole to another. Inside the shell, there will be a network of strings.

Can one split this network into basic components? Can one say that such a random network is, in some sense, made of:

  1. lone string segments,
  2. touching pairs of skew strings,
  3. touching sets of three strings,
  4. nothing else?

(Twists and braids being included in 2.) Is this enumeration complete?

Alternatively, can one say what defects are possible in such a network? A tentative list being:

A. open links/tangles,

B. nothing else?

(Knots not being possible, nor anything else?)


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