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A filtered generalization of the Chekanov-Eliashberg algebra
Russell Avdek
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We define a new algebra associated to a Legendrian submanifold Λ of a contact manifold of the form ℝₜ ×W, called the planar diagram algebra and denoted PDA(Λ, 𝒫). It is a non-commutative, filtered, differential graded algebra whose filtered stable tame isomorphism class is an invariant of Λ together with a partition 𝒫 of its connected components. When Λ is connected, PDA is the Chekanov-Eliashberg algebra. In general, the PDA differential counts holomorphic disks with multiple positive punctures using a combinatorial framework inspired by string topology.
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