Fueter equations and the search for a higher dimensional Hamiltonian Floer theory I: analytical foundations and compactness

2026/03/02 by L. Asselle, R. Brilleslijper · 1 voice
Mathematics · #math.SG #math.AP

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Abstract

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], which provides a Hamiltonian description of harmonic maps for which the associated equations are elliptic, we analyze the compactness of the associated moduli spaces of Fueter maps. For compact quotients Q of complex hyperbolic space, we exploit the structure of the Biquard-Gauduchon hyperkähler metric to prove relative compactness under suitable smallness assumptions on the Hamiltonian. In the flat case, we establish the necessary quantitative L^∞-estimates and outline a perturbative strategy for the non-flat setting.

Citations

• Morse homology for a class of elliptic partial differential equations
• Generalizing symplectic topology from 1 to 2 dimensions
• Towards a monopole Fueter Floer homology I: a compactness theorem
• A compactness theorem for Fueter sections
• Methods of Differential Geometry in Classical Field Theories: k-symplectic and k-cosymplectic approaches
• Cuplength estimates in Morse cohomology
• Hypercontact structures and Floer homology
• Hyperkaehler structures on total spaces of holomorphic cotangent bundles
• The Existence of Minimal Immersions of 2-Spheres

Discussions

• L. Asselle, R. Brilleslijper: Fueter equations and the search for a higher dimensional Hamiltonian Floer theory I: analytical foundations and compactness https://arxiv.org/abs/2603.01832 https://arxiv [bsky, 0 points, 0 comments]

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