Infinitely many exotic monotone Lagrangian tori in ℂℙ2
By Renato Vianna. 2014
67 citations recorded by the source corpus.
In [10], we construct an exotic monotone Lagrangian torus in CP 2 (not Hamiltonian isotopic to the known Clifford and Chekanov tori) using techniques motivated by mirror symmetry. We named it T(1,4,25) because, when following a degeneration of CP 2 to the orbifold CP(1,4,25), it degenerates to the central fiber of the moment map for the standard torus action on CP(1,4,25). Related to each degeneration from CP 2 to CP(a 2 ,b 2 ,c 2 ), for (a,b,c) a Markov triple - see (1.1) - there is a monotone Lagrangian torus, which we call T(a 2 ,b 2 ,c 2 ). We conjectured that no two of them are Hamiltonian isotopic to each other. Here we employ techniques from symplectic field theory to prove that the above conjecture is true.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/d93a476d3334b875844ea5f94451b9316f4c072b
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Citations in the corpus
- Infinitely many Lagrangian fillings (2020, background): “10], k ≥ 3, and infinitely many exact Lagrangian tori were known to exist in certain Stein surfaces by using either of the articles [39, 57, 61, 62].”