Departmental Seminar

Tangling: between geometry and topology

Professor Stephen Hyde
AM Department RSP

Tangled structures seem to occur at all length scales, from shoelaces to DNA. Molecular tangles, from weavings to knots and catenated nets, are being synthesised, and observed in vitro (and in vivo), in labs around the world. We need a grammar of tangling. We have been developing a constructive account of tangles, that builds on a simple observation: the simplest tangle is a double-helix. Multiple double-helices can be wired together to build more complex tangles. And single-,triple-,..helices can be added to the mix. The description views a tangle as a multi-track railway winding around a surface. We tune the number of tracks and the twist to generate tangles. The simplest railways gives knots. More complex railways lead to tangled nets, and exotic tangling containing nets, filaments, loops, etc. We are looking for a “grand unification” of the whole mess; the twin concepts of winding and topology get us a long way. Railways have a natural encoding, reminiscent of protein and RNA or DNA folding.

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