Symplectic -manifolds I: Filtration on Quantum Cohomology

AF Ritter, F Živanović - arXiv preprint arXiv:2304.13026, 2023 - arxiv.org
We define a large new class of open symplectic manifolds, which includes all Conical
Symplectic Resolutions. They come with a pseudoholomorphic $\mathbb {C}^* $-action …

Symplectic -manifolds II: Morse-Bott-Floer Spectral Sequences

AF Ritter, F Živanović - arXiv preprint arXiv:2304.14384, 2023 - arxiv.org
In Part I, we defined a large class of open symplectic manifolds, called symplectic $\mathbb
{C}^* $-manifolds, which are typically non-exact at infinity, and we showed that their …

Invariance of symplectic cohomology and twisted cotangent bundles over surfaces

G Benedetti, AF Ritter - International Journal of Mathematics, 2020 - World Scientific
We prove that symplectic cohomology for open convex symplectic manifolds is invariant
when the symplectic form undergoes deformations which may be nonexact and …

On the filtered symplectic homology of prequantization bundles

VL Ginzburg, J Shon - International Journal of Mathematics, 2018 - World Scientific
We study Reeb dynamics on prequantization circle bundles and the filtered (equivariant)
symplectic homology of prequantization line bundles, aka negative line bundles, with …

On fillings of contact links of quotient singularities

Z Zhou - Journal of Topology, 2024 - Wiley Online Library
We study several aspects of fillings for links of general isolated quotient singularities using
Floer theory, including co‐fillings, Weinstein fillings, strong fillings, exact fillings and exact …

[PDF][PDF] Extensible positive loops and vanishing of symplectic cohomology

D Cant, J Hedicke, E Kilgore - arXiv preprint arXiv:2311.18267, 2023 - researchgate.net
The symplectic cohomology of certain symplectic manifolds W with non-compact ends
modelled on the positive symplectization of a compact contact manifold Y is shown to vanish …

Two closed orbits for non-degenerate Reeb flows

M Abreu, J Gutt, J Kang, L Macarini - Mathematical Proceedings of …, 2021 - cambridge.org
We prove that every non-degenerate Reeb flow on a closed contact manifold M admitting a
strong symplectic filling W with vanishing first Chern class carries at least two geometrically …

Automatic transversality in contact homology II: filtrations and computations

J Nelson - Proceedings of the London Mathematical Society, 2020 - Wiley Online Library
This paper is the sequel to the previous paper [Nelson, Abh. Math. Semin. Univ. Hambg. 85
(2015) 125–179], which showed that sufficient regularity exists to define cylindrical contact …

On the mean Euler characteristic of Gorenstein toric contact manifolds

M Abreu, L Macarini - International Mathematics Research …, 2020 - academic.oup.com
We prove that the mean Euler characteristic of a Gorenstein toric contact manifold, that is, a
good toric contact manifold with zero 1st Chern class, is equal to half the normalized volume …

An intertwining relation for equivariant Seidel maps

T Liebenschutz-Jones - arXiv preprint arXiv:2010.03342, 2020 - arxiv.org
The Seidel maps are two maps associated to a Hamiltonian circle action on a convex
symplectic manifold, one on Floer cohomology and one on quantum cohomology. We …