39 citations · 140 across the 18 of their papers we have counts for
4 papers · 2 filters
Global surfaces of section for Reeb flows in dimension three and beyond
Umberto L. Hryniewicz, Pedro A. S. Salomão
We survey some recent developments in the quest for global surfaces of section for Reeb flows in dimension three using methods from Symplectic Topology. We focus on applications to…
Systolic ratio, index of closed orbits and convexity for tight contact forms on the three-sphere
Alberto Abbondandolo, Barney Bramham, Umberto Hryniewicz +1
We construct a dynamically convex contact form on the three-sphere whose systolic ratio is arbitrarily close to 2. This example is related to a conjecture of Viterbo, whose validit…
Contact forms with large systolic ratio in dimension three
Alberto Abbondandolo, Barney Bramham, Umberto L. Hryniewicz +1
The systolic ratio of a contact form on a closed three-manifold is the quotient of the square of the shortest period of closed Reeb orbits by the contact volume. We show that every…
Transversality for local Morse homology with symmetries and applications
Doris Hein, Umberto L. Hryniewicz, Leonardo Macarini
We prove the transversality result necessary for defining local Morse chain complexes with finite cyclic group symmetry. Our arguments use special regularized distance functions co…