All Questions

While preparing for my introduction to topology course, I've realized that I don't know where to find a detailed proof of the Reidemeister theorem (two link diagrams give isotopic links, iff they can ...

Connect $n$ random points on a sphere in a cycle of segments between succesive points: I would like to know the growth rate, with respect to $n$, of the crossing number (the minimal number of ...

Question: Given a `hard' diagram of a knot, with over a hundred crossings, what is the best algorithm and software tool to simplify it? Will it also simplify virtual knot diagrams, tangle diagrams, ...

Definitions: A knot is an embedding $\kappa:S^1\hookrightarrow S^3$ (we do not require smooth or polygonal). Two knots $\kappa,\,\lambda:S^1\hookrightarrow S^3$ are equivalent if one of the following ...

The classical PL Reidemeister Theorem reads: Reidemeister Theorem: Two knots in $S^3$ are PL ambient isotopic if and only if any diagram of one can be transformed into a diagram of the other by ...