SymCoTop: Symplectic and Contact Topology

Project funded by Fundação para a Ciência e a Tecnologia, I.P. (FCT) (Concurso de Projetos Exploratórios em Todos os Domínios Científicos 2023), grant 2023.13969.PEX. Funded amount: EUR 49,858.60, as stated by the source. Runs 2025-02-01 to 2026-07-31. Keywords: symplectic embeddings, tautological bundles, quantum homology, contact homology, Exact sciences. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2025-07-21); national funding data, not CORDIS; selected because its keywords name quantum. Abstract given by the source: Symplectic geometry emerged initially as the geometry of classical mechanics but underwent a revolution around 1985 by Gromov [Gr], who introduced J-holomorphic techniques, proving exceptional results such as the famous Nonsqueezing Theorem. Since then, this field has developed its own identity, witnessing significant progress in both longstanding and novel inquiries. Nowadays, symplectic geometry is a rich and exciting field with many connections to other disciplines, including algebraic and complex geometry, low-dimensional topology, dynamical systems, PDEs, mirror symmetry, and string theory. The focus on global properties holds paramount importance for the entire subject of symplectic topology. A fundamental result in this field is Darboux's Theorem , which states that every symplectic manifold is locally isomorphic to the Euclidean space of the corresponding dimension with its standard symplectic structure. Consequently, there cannot be any local invariants that distinguish symplectic manifolds. The absence of local invariants allows for the existence of an extensive, infinite-dimensional group of diffeomorphisms preserving the symplectic structure, known as symplectomorphisms . This contrasts sharply with a Riemannian manifold, where the group of isometries is finite dimensional, and curvature serves as a local invariant. On the other hand, in one of the several lines of development initiated by Gromov, in 1985 [Gr], he proved one of his most renowned results, the Nonsqueezing Theorem , which asserts that a symplectic image of a ball cannot be ‘long and thin’, which means there is no symplectic embedding of a standard ball of radius r into a symplectic cylinder of radius R whenever R < r. This reveals the presence of global obstructions, beyond volume considerations, for embedding large balls in symplectic manifolds. The Nonsqueezing Theorem is also reflected in the properties of the symplectomorphism group. In the late 1970s, Eliashberg [EL1, El2] proved [shortened; the full text is on the OpenAIRE page]

Original source.

Source: OpenAIRE Graph: projects of national funders, OpenAIRE, from the project data of Fundação para a Ciência e a Tecnologia, I.P. (FCT). Retrieved 2026-10-28. Licence: Creative Commons Attribution 4.0 (OpenAIRE Graph). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: Creative Commons Attribution 4.0 (CC BY 4.0).

AI-assisted summary: The SymCoTop project, funded by FCT with a grant of EUR 49,858.60, runs from February 1, 2025, to July 31, 2026. It explores symplectic geometry and its connections to various scientific disciplines, including quantum homology. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.