Russell Avdek

collaborators

4 papers

math.SG2026

Symplectic mapping class relations from pencil pairs

Russell Avdek

We describe symplectic mapping class relations between products of positive Dehn twists along Lagrangian spheres in Weinstein $4$ -manifolds, all of which are affine $C$ va…

math.SG2024

A filtered generalization of the Chekanov-Eliashberg algebra

Russell Avdek

We define a new algebra associated to a Legendrian submanifold $I^$ of a contact manifold of the form $R_{t} \times W$ , called the planar diagram algebra and denoted $PDA(…

math.SG2024

Stabilization of divisors in high-dimensional contact manifolds

Russell Avdek

A stabilization operation is defined for codimension $2$ contact submanifolds in $dim \geq 5$ contact manifolds $(M, I^¾)$ . The definition is such that (1) a given $(M, I^¾)$ is ove…

math.SG2024

Bourgeois' contact manifolds are tight

Russell Avdek, Zhengyi Zhou

We prove that Bourgeois' contact structures on $M \times T^{2}$ determined by the supporting open books of a contact manifold $(M, I^¾)$ are always tight. The proof is base…