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This research aims to investigate the geometric filtration of the Lagrangian cobordism group associated with symplectic manifolds.

August 2, 2026Advances in MathematicsOpen Access

Fourier transforms and a filtration on the Lagrangian cobordism group of tori

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Randomized trial reveals geometric structure in Lagrangian cobordism, suggesting connections to abelian varieties.

This research aims to investigate the geometric filtration of the Lagrangian cobordism group associated with symplectic manifolds.
Constructed a geometric filtration of finite length for the fibered Lagrangian cobordism group.
Developed a Fourier transform between Fukaya categories of dual symplectic tori.
Established a connection to derived categories of coherent sheaves on dual abelian varieties under homological mirror symmetry.
Demonstrated that the Lagrangian cobordism group admits a finite-length geometric filtration.
Showed the correspondence between the Fourier transform and the Bloch filtration on Chow groups of abelian varieties.
Confirmed implications for broader mathematical contexts beyond the initial results.

Álvaro Muñiz-Brea (2026) studied this question.

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