6 papers
Fueter equations and the search for a higher dimensional Hamiltonian Floer theory I: analytical foundations and compactness
L. Asselle, R. Brilleslijper
We study a Floer-theoretic approach to harmonic maps from the two-torus into non-flat Kähler manifolds. Building on the complex-regularized polysymplectic (CRPS) formalism of [BF24…
Floer sections in multisymplectic geometry
Ronen Brilleslijper, Oliver Fabert
In symplectic geometry, Floer theory is the most important tool to prove the existence of time-periodic solutions in Hamiltonian mechanics. The core observation is that the -g…
Generalizing symplectic topology from 1 to 2 dimensions
Ronen Brilleslijper, Oliver Fabert
In symplectic topology one uses elliptic methods to prove rigidity results about symplectic manifolds and solutions of Hamiltonian equations on them, where the most basic example i…
An approach to Hamiltonian Floer theory for maps from surfaces
Ronen Brilleslijper, Oliver Fabert
In -dimensional classical field theory one studies maps from -dimensional manifolds in such a way that classical mechanics is recovered for . In previous papers we have…
From Euclidean field theory to hyperkähler Floer theory via regularized polysymplectic geometry
Ronen Brilleslijper, Oliver Fabert
Hamiltonian Floer theory plays an important role for finding periodic solutions of Hamilton's equation, which can be seen as a generalization of Newton's equation. Generalizing New…
Regularized polysymplectic geometry and first steps towards Floer theory for covariant field theories
Ronen Brilleslijper, Oliver Fabert
It is the goal of this paper to present the first steps for defining the analogue of Hamiltonian Floer theory for covariant field theory, treating time and space relativistically.…