On the Lagrangian Hofer geometry of Clifford tori

2025/08/04 by Frol Zapolsky, Zapolsky, Frol · 1 citation
Mathematics · #53D99 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2508.02501

openalex publication_date 2025/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the space of Lagrangians which are Hamiltonian isotopic to the Clifford torus in a complex projective space or in the four-dimensional quadric, taken with Chekanov's Lagrangian Hofer metric, contains a quasi-isometric copy of the real line, and in particular has infinite diameter.

Citations

• Hofer distance on Lagrangian links inside the disc
• Hofer geometry of A₃-configurations
• Spectral invariants over the integers
• The unbounded Lagrangian spectral norm and wrapped Floer cohomology
• Spectral invariants for monotone Lagrangians
• Orientations for pseudoholomorphic quilts
• On a family of Lagrangian submanifolds in bidisks and Lagrangian Hofer metric
• Symplectic quasi-states on the quadric surface and Lagrangian submanifolds
• Notes on monotone Lagrangian twist tori
• Quantum Structures for Lagrangian Submanifolds
• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
• Construction of spectral invariants of Hamiltonian paths on closed symplectic manifolds
• Calabi quasimorphism and quantum homology
• The geometry of symplectic energy

Cited by

• On link quasimorphisms on the sphere and the equator conjecture

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• Monodromy and isotopy of monotone Lagrangian tori
• On the Lagrangian Hofer geometry in symplectically aspherical manifolds