A symplectic basis for 3-manifold triangulations
Geometric Topology
2025-09-01 v1
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.
Cite
@article{arxiv.2208.06969,
title = {A symplectic basis for 3-manifold triangulations},
author = {Daniel V. Mathews and Jessica S. Purcell},
journal= {arXiv preprint arXiv:2208.06969},
year = {2025}
}
Comments
45 pages, 19 figures