arXiv subjects

Levi Ryffel

Publications and source records attributed to Levi Ryffel.

4 recordsLinked to original sources

arXiv2023

Trefoils and hexafoils in 3-braids

We determine the cobordism distance between all positive 3-braid links and connected sums of trefoil knots, up to a constant error. This may be seen as a reinterpretation of Coxeter's finiteness result on the braid group on three strands modulo third powers of the generators. We go on to explore the limits of Coxeter's result, and find the cobordism distance between three strand torus links and almost all connected sums of two strand torus links, up to a constant error.

math.GT↗

arXiv2022

Two strand twisting

We prove that fibred knots cannot be untied with $\bar{t}_{2k}$-moves, for all $k \geq 2$. More generally, we give an upper bound on the number of two strand twist operations that allow to untie a knot with non-trivial HOMFLY polynomial, in terms of the minimal crossing number, and the braid index. As a by-product, we prove that the braid index of a two-bridge knot cannot be lowered by applying $t_{2k}$-moves, for all but finitely many $k \in \mathbb{N}$.

math.GT↗

arXiv2022

Curves intersecting in a circuit pattern

We show that the cycle relation between Dehn twists about curves in a circuit detects whether the circuit bounds an embedded disc. This is done by determining the isomorphism type of the group generated by said Dehn twists for various surfaces.

math.GT↗

arXiv2020

Bouquets of curves in surfaces

We characterise when a set of simple closed curves in an orientable surface forms a bouquet, in terms of relations between the corresponding Dehn twists.

math.GT↗