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In the 1980s, Neumann and Zagier introduced a symplectic vector spaceassociated to an ideal triangulation of a cusped 3-manifold, such as a knotcomplement. We give a geometric interpretation for this symplectic structure interms of the topology of the 3-manifold, via intersections of certain curves ona Heegaard surface. We also give an algorithm to construct curves forming asymplectic basis.

A symplectic basis for 3-manifold triangulations