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A natural framing of knots


Research objectives and content To deepen the understanding of how many intersections of which sign of boundary with interior a disk in 3-space must have, depending on the knot type of the boundary; to study the relations between these numbers, and other, better known knot invariants, and how they reflect the interactions between the topological and geometric properties of knots. More specifically, to illuminate the relation between the 'natural framing number', the signature, and the unknotting number of knots, to calculate the natural framing of Seifert fibred knots, to give formulae for satellite- and two bridge knots, and, in the case of hyperbolic knots, to investigate the geometric meaning of the natural framing number. Training content (objective, benefit and expected impact) To deepen my understanding of the geometric properties of knots and knot groups. To establish myself as a researcher in geometric topology and 3-manifold theory, by way of profiting from and contributing to the team of topologists at the U Provence. Links with industry / industrial (22)


Rue Joliot Curie 39 Cnrs Umr 6632
13453 Marseille