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Bilinearized Legendrian contact homology and the augmentation category. (English) Zbl 1308.53119

The authors present the algebraic construction of the augmentation category for any semi-free differential graded algebra (DGA). Then, they apply this algebraic construction to the case of the Chekanov algebra of a Legendrian submanifold. The authors also give a geometrical interpretation of the bilinearized differential in terms of the Chekanov algebra of the 2-copy Legendrian link. The generalization of the duality exact sequence from [T. Ekholm et al., Duke Math. J. 150, No. 1, 1–75 (2009; Zbl 1193.53179)] is also investigated. Next, the authors interpret the bilinearized Legendrian contact homology in terms of Floer homology of Lagrangian fillings, as defined in [T. Ekholm, Prog. Math. 296, 109–145 (2012; Zbl 1254.57024)]. Finally, some simple examples of computations are presented (Trefoil knot and Chekanov-Eliashberg knot).

MSC:

53D12 Lagrangian submanifolds; Maslov index
53D40 Symplectic aspects of Floer homology and cohomology
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