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The Lagrangian cobordism group of T2T^2

Abstract

We compute the Lagrangian cobordism group of the standard symplectic 2-torus and prove that it is isomorphic to the Grothendieck group of its derived Fukaya category. The proofs use homological mirror symmetry for the 2-torus.Comment: 43 pages, 12 figures. V2: Result of computation of the cobordism group reformulated; further minor changes and corrections. V3: Updated such as to agree with accepted version. To appear in Selecta Mathematic

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