Coisotropic rigidity and $C^{0}$-symplectic geometry
By Vincent Humilière, R. Leclercq, Sobhan Seyfaddini. 2013
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We prove that symplectic homeomorphisms, in the sense of the celebrated Gromov-Eliashberg Theorem, preserve coisotropic submanifolds and their characteristic foliations. This result generalizes the Gromov-Eliashberg Theorem and demonstrates that previous rigidity results (on Lagrangians by Laudenbach-Sikorav, and on characteristics of hypersurfaces by Opshtein) are manifestations of a single rigidity phenomenon. To prove the above, we establish a C^0-dynamical property of coisotropic submanifolds which generalizes a foundational theorem in C^0-Hamiltonian dynamics: Uniqueness of generators for continuous analogs of Hamiltonian flows.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/170a5cbb962fe0dc9a17cf3c49f1a34686f208fc
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In Geometry and Topology
In Mathematical Physics
In Statistical and Nonlinear Physics
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- Bounds on spectral norms and barcodes (2018, background): “Theorem 12.4.4],[111, Remark 2.2]). The Lagrangian spectral norm (L; ) was introduced in [118] for L= 0 Q;the zero section in the cotangent bundle M= TQ;wherein its nondegeneracy was proven (see also [60, 69, 77]). Since the introduction of Lagrangian spectral invariants [64, 65] for weakly monotone”
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