Examples around the strong Viterbo conjecture
A strong version of a conjecture of Viterbo asserts that all normalized symplectic capacities
agree on convex domains. We review known results showing that certain specific …
agree on convex domains. We review known results showing that certain specific …
Symplectic capacities of domains close to the ball and Banach-Mazur geodesics in the space of contact forms
A Abbondandolo, G Benedetti, O Edtmair - arXiv preprint arXiv …, 2023 - arxiv.org
We prove that all normalized symplectic capacities coincide on smooth domains in $\mathbb
C^ n $ which are $ C^ 2$-close to the Euclidean ball, whereas this fails for some smooth …
C^ n $ which are $ C^ 2$-close to the Euclidean ball, whereas this fails for some smooth …
Higher symplectic capacities
K Siegel - arXiv preprint arXiv:1902.01490, 2019 - arxiv.org
We construct a new family of symplectic capacities indexed by certain symmetric
polynomials, defined using rational symplectic field theory. We prove various structural …
polynomials, defined using rational symplectic field theory. We prove various structural …
Lusternik–Schnirelmann theory and closed Reeb orbits
VL Ginzburg, BZ Gürel - Mathematische Zeitschrift, 2020 - Springer
We develop a variant of Lusternik–Schnirelmann theory for the shift operator in equivariant
Floer and symplectic homology. Our key result is that the spectral invariants are strictly …
Floer and symplectic homology. Our key result is that the spectral invariants are strictly …
On the Hochschild cohomology of Tamarkin categories
arXiv:2312.11447v1 [math.SG] 18 Dec 2023 On the Hochschild cohomology of Tamarkin
categories Page 1 arXiv:2312.11447v1 [math.SG] 18 Dec 2023 On the Hochschild cohomology …
categories Page 1 arXiv:2312.11447v1 [math.SG] 18 Dec 2023 On the Hochschild cohomology …
3D convex contact forms and the Ruelle invariant
J Chaidez, O Edtmair - Inventiones mathematicae, 2022 - Springer
Abstract Let X⊂ R 4 be a convex domain with smooth boundary Y. We use a relation
between the extrinsic curvature of Y and the Ruelle invariant of the Reeb flow on Y to prove …
between the extrinsic curvature of Y and the Ruelle invariant of the Reeb flow on Y to prove …
Symplectic cohomology and a conjecture of Viterbo
E Shelukhin - Geometric and Functional Analysis, 2022 - Springer
We identify a new class of closed smooth manifolds for which there exists a uniform bound
on the Lagrangian spectral norm of Hamiltonian deformations of the zero section in a unit …
on the Lagrangian spectral norm of Hamiltonian deformations of the zero section in a unit …
Equivariant symplectic homology, linearized contact homology and the Lagrangian capacity
M Pereira - arXiv preprint arXiv:2205.13381, 2022 - arxiv.org
We establish computational results concerning the Lagrangian capacity from" Cieliebak and
Mohnke-Punctured holomorphic curves and Lagrangian embeddings". More precisely, we …
Mohnke-Punctured holomorphic curves and Lagrangian embeddings". More precisely, we …
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 Resolutions. They come with a pseudoholomorphic $\mathbb {C}^* $-action …
Computing higher symplectic capacities I
K Siegel - International Mathematics Research Notices, 2022 - academic.oup.com
We present recursive formulas that compute the recently defined “higher symplectic
capacities” for all convex toric domains. In the special case of four-dimensional ellipsoids …
capacities” for all convex toric domains. In the special case of four-dimensional ellipsoids …