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CORDIS

Homeomorphisms in symplectic topology and dynamics

Project description

Advancing the field of continuous symplectic topology

Continuous symplectic topology studies continuous analogues of smooth symplectic objects, such as symplectic and Hamiltonian homeomorphisms, and investigates the persistence of various symplectic phenomena under uniform limits and perturbations. The EU-funded HSD project will explore continuous symplectic topology from two different perspectives. The first is a symplectic topological perspective that is informed by Gromov’s soft and hard symplectic geometry. The second one is motivated by the recent interactions of continuous symplectic topology and dynamical systems, which fall under the new field of symplectic dynamics.

Objective

The subject of this proposal is the field of continuous symplectic topology. This is an area of symplectic topology which defines and studies continuous analogues of smooth symplectic objects such as symplectic and Hamiltonian homeomorphisms and asks questions about persistence of various symplectic phenomena under uniform limits and perturbations.

Our aim is to explore, and further develop, continuous symplectic topology from two different perspectives: The first is a symplectic topological perspective which is informed by Gromov’s soft and hard view of symplectic topology. The second is motivated by the recent interactions of continuous symplectic topology and dynamical systems and it falls under the new field of symplectic dynamics.

We outline an extensive research program in line with the above two viewpoints. On the one hand, we propose to develop new tools for the advancement of the field via the medium of barcodes which will serve as a replacement of Floer homology for homeomorphisms. On the other hand, we propose new approaches towards several important questions in the field including the symplectic four-sphere problem which asks if non-symplectic manifolds, such as the four-sphere, could admit the structure of a topological symplectic manifold, and the simplicity conjecture which asks if the group of compactly supported area-preserving homeomorphisms of the disc is a simple group.

Host institution

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Net EU contribution
€ 1 340 472,00
Address
RUE MICHEL ANGE 3
75794 Paris
France

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Region
Ile-de-France Ile-de-France Paris
Activity type
Research Organisations
Links
Total cost
€ 1 340 472,00

Beneficiaries (1)