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CPP: Fachverband Chemische Physik und Polymerphysik
CPP 15: Poster I
CPP 15.43: Poster
Monday, March 18, 2024, 18:00–20:00, Poster C
Knot diagrams for 3-periodic entanglements. — •Toky Andriamanalina1, Myfanwy Evans1, and Sonia Mahmoudi2 — 1University of Potsdam, Germany — 2Tohoku University, Japan
Polymers, DNA origami crystals, and many other biological and chemical structures present features of entanglement, arranging in a 3-periodic fashion. As the topology of those structures have influence on their physical properties, some knot invariants have been extended into measures, such as the periodic linking number or the periodic Jones polynomials, to quantify the entanglement. This project aims to give a new mathematical diagrammatic description based on Knot theory for 3-periodic entangled structures. To do so, we project a unit cell of the structure onto a square with periodic boundaries. To the projected curves, we add crossing information, and we introduce new symbols to capture the periodic boundary conditions of the unit cell. The new diagrams require a set of new moves added to the three usual Reidemeister moves.
Keywords: crystal; entanglement; knots; topology; mathematics