A survey on orderability and contact non-squeezing

2025/04/16 by Igor Uljarević, Uljarević, Igor · 1 voice
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Holomorphic and Operator Theory #Multi-Criteria Decision Making #Symplectic Geometry (math.SG) #math.SG

paper · pdf · doi:10.48550/arxiv.2504.12061

openalex publication_date 2025/04/16 · arxiv published 2025/04/16 · arxiv updated 2025/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The present article provides an overview of Yakov Eliashberg's seminal contributions to the concepts of orderability and contact non-squeezing. It also examines subsequent research by various authors, highlighting the significance of these notions and offering a detailed account of the current state of the field.

Citations

• On the topology of loops of contactomorphisms and Legendrians in non-orderable manifolds
• Selective Floer cohomology for contact vector fields
• Rabinowitz Floer homology for prequantization bundles and Floer Gysin sequence
• Contact non-squeezing at large scale via generating functions
• Spectral selectors and contact orderability
• Contact non-squeezing and orderability via the shape invariant
• Quasi-morphisms on contactomorphism groups and Grassmannians of 2-planes
• Tight neighborhoods of contact submanifolds
• Contact orderability up to conjugation
• Givental's non-linear Maslov index on lens spaces
• Positive Legendrian isotopies and Floer Theory
• The Bott-Samelson theorem for positive Legendrian isotopies
• A simple construction of positive loops of Legendrians
• On positive loops of loose Legendrian embeddings
• Chern-Weil theory and the group of strict contactomorphisms
• On the strong orderability of overtwisted 3-folds
• Non-squeezing property of contact balls
• Symplectic cohomology and Viterbo's theorem
• Brieskorn manifolds in contact topology
• Quasi-morphisms on contactomorphism groups and contact rigidity
• Slow volume growth for Reeb flows on spherizations and contact Bott--Samelson theorems
• Universal orderability of Legendrian isotopy classes
• Orderable Contact Structures on Liouville-fillable Contact Manifolds
• Orderability, contact non-squeezing, and Rabinowitz Floer homology
• The discriminant and oscillation lengths for contact and Legendrian isotopies
• The Action homomorphism, quasimorphisms and moment maps on the space of compatible almost complex structures
• Spectral invariants with bulk, quasimorphisms and Lagrangian Floer theory
• A variational approach to Givental's nonlinear Maslov index
• Deformed Hamiltonian Floer theory, capacity estimates, and Calabi quasimorphisms
• Sheaf quantization of Hamiltonian isotopies and applications to non displaceability problems
• Positive isotopies of Legendrian submanifolds and applications
• Topological quantum field theory structure on symplectic cohomology
• Equivariant Homology of Generating Functions and Orderability of Lens Spaces
• Non-negative Legendrian isotopy in ST^*M
• Rabinowitz Floer homology and symplectic homology
• Contact Homology, Capacity and Non-Squeezing in R²n x S¹ via Generating Functions
• Legendrian links, causality, and the Low conjecture
• Geometry of contact transformations and domains: orderability versus squeezing
• On the Floer homology of cotangent bundles
• Floer Homology and the Heat Flow
• Commutator length of symplectomorphisms
• Partially ordered groups and geometry of contact transformations
• Pseudo holomorphic curves in symplectic manifolds

Discussions

• Igor Uljarevi\'c: A survey on orderability and contact non-squeezing https://arxiv.org/abs/2504.12061 https://arxiv.org/pdf/2504.12061 https://arxiv.org/html/2504.12061 [bsky, 0 points, 1 comments]

Related

• Contact non-squeezing in various closed prequantizations
• Tight and overtwisted contact structures
• Squeezing: from numerical to conceptual problems
• New Results for the Two-Stage Contact Process
• RECENT DEVELOPMENTS IN THE PINCH TECHNIQUE