Index action filtration, 64 adjacent elements of a poset, 105 algebraic intersection number, 63 annulus reduction, 23 arc condition, 13, 39 bottom boundary, 37 boundary, 8 broken heart, 69 cancellation formula, 14, 23 catenation, 11, 39 chain, 7 combinatorial Floer homology, 63 lune, 40 compatible hearts, 71 connection matrix, 106 counting function of a lune, 37 diamonds, 89 embedded lune, 37, 45 end of a lune, 47 endpoints of a lune, 37 equator, 91 equivalent broken hearts, 69 holomorphic strips, 81 lunes, 37 smooth hearts, 70 existence of a lune, 40 Floer chain complex, 63, 103 Floer homology, 63, 89 analytic, 89 combinatorial, 63 dimension, 64 triangle product, 92 geometric intersection number, 63 grading integer, 66 mod two, 65 heart broken, 69 midpoint of, 69 smooth, 70 hearts and diamonds, 89 compatible, 71 equivalent, 69, 70 of type (ac) and (bd), 70 index formula, 83 index function on a poset, 106 integer coeﬃcients, 66 grading, 66 intersection number, 63 algebraic, 63 geometric, 63 numerical, 63 isotopy argument, 25 left end of a lune, 47 linear index formula, 85 lune combinatorial, 40 counting function of, 37 embedded, 37 endpoints of, 37 existence, 40 left end of, 47 right end of, 47 smooth, 37 uniqueness, 40 lunes equivalent, 37 Maslov index, 13, 39 midpoint of a heart, 69 mod two grading, 65 numerical intersection number, 63 planar 2-manifold, 15 primitive trace, 45 reduced (α, β)-trace, 21 113

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