A symplectic basis for 3-manifold triangulations

2022/08/15 by Mathews, Daniel V., Purcell, Jessica S.
#57K30 #57K31 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2208.06969

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.

Related

• Layered-triangulations of 3-manifolds
• Reconstructing triangulations of 3-manifolds from their intersection matrix
• Triangulated Manifolds with Few Vertices: Geometric 3-Manifolds
• 3-manifolds as viewed from the curve complex
• Symplectic forms on trisected 4-manifolds