Symplectic capacities from positive S1–equivariant symplectic homology
J Gutt, M Hutchings - Algebraic & geometric topology, 2018 - msp.org
We use positive S 1–equivariant symplectic homology to define a sequence of symplectic
capacities ck for star-shaped domains in ℝ 2 n. These capacities are conjecturally equal to …
capacities ck for star-shaped domains in ℝ 2 n. These capacities are conjecturally equal to …
Symplectic embedding problems, old and new
F Schlenk - Bulletin of the American Mathematical Society, 2018 - ams.org
Symplectic embedding problems, old and new Page 1 BULLETIN (New Series) OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 55, Number 2, April 2018, Pages 139–182 …
AMERICAN MATHEMATICAL SOCIETY Volume 55, Number 2, April 2018, Pages 139–182 …
Symplectic embeddings from concave toric domains into convex ones
D Cristofaro-Gardiner - Journal of Differential Geometry, 2019 - projecteuclid.org
Embedded contact homology gives a sequence of obstructions to four-dimensional
symplectic embeddings, called ECH capacities. In “Symplectic embeddings into four …
symplectic embeddings, called ECH capacities. In “Symplectic embeddings into four …
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 …
Proof of the simplicity conjecture
D Cristofaro-Gardiner, V Humilière… - arXiv preprint arXiv …, 2020 - arxiv.org
In the 1970s, Fathi, having proven that the group of compactly supported volume-preserving
homeomorphisms of the $ n $-ball is simple for $ n\ge 3$, asked if the same statement holds …
homeomorphisms of the $ n $-ball is simple for $ n\ge 3$, asked if the same statement holds …
Proof of the simplicity conjecture
D Cristofaro-Gardiner, V Humilière… - Annals of …, 2024 - projecteuclid.org
In the 1970s, Fathi, having proven that the group of compactly supported volume-preserving
homeomorphisms of the n-ball is simple for n≥3, asked if the same statement holds in …
homeomorphisms of the n-ball is simple for n≥3, asked if the same statement holds in …
Computing embedded contact homology in Morse-Bott settings
Y Yao - arXiv preprint arXiv:2211.13876, 2022 - arxiv.org
Given a contact three manifold $ Y $ with a nondegenerate contact form $\lambda $, and an
almost complex structure $ J $ compatible with $\lambda $, its embedded contact homology …
almost complex structure $ J $ compatible with $\lambda $, its embedded contact homology …
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 …
An elementary alternative to ECH capacities
M Hutchings - Proceedings of the National Academy of …, 2022 - National Acad Sciences
The embedded contact homology (ECH) capacities are a sequence of numerical invariants
of symplectic four-manifolds that give (sometimes sharp) obstructions to symplectic …
of symplectic four-manifolds that give (sometimes sharp) obstructions to symplectic …
Beyond ECH capacities
M Hutchings - Geometry & Topology, 2016 - msp.org
ECH (embedded contact homology) capacities give obstructions to symplectically
embedding one four-dimensional symplectic manifold with boundary into another. These …
embedding one four-dimensional symplectic manifold with boundary into another. These …