A symplectic basis for 3-manifold triangulations

Daniel V. Mathews; Jessica S. Purcell

doi:10.4310/cag.250813161542

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arXiv · 2208.06969

A symplectic basis for 3-manifold triangulations

Daniel V. Mathews·Jessica S. Purcell

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Abstract

In the 1980s, Neumann and Zagier introduced a symplectic vector space associated to an ideal triangulation of a cusped 3-manifold, such as a knot complement. We give a geometric interpretation for this symplectic structure in terms of the topology of the 3-manifold, via intersections of certain curves on a Heegaard surface. We also give an algorithm to construct curves forming a symplectic basis.

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Daniel V. Mathews, Jessica S. Purcell. 2022-08-15. A symplectic basis for 3-manifold triangulations. https://doi.org/10.4310/cag.250813161542

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