A symplectic basis for 3-manifold triangulations

Daniel V. Mathews; Jessica S. Purcell

doi:10.4310/CAG.250813161542

A symplectic basis for 3-manifold triangulations

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

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. This has been reinterpreted geometrically in a number of ways. Here, we give an effective, algorithmic way to construct curves forming a symplectic basis directly from the ideal triangulation of the 3-manifold.

Original language	English
Pages (from-to)	815-878
Number of pages	64
Journal	Communications in Analysis and Geometry
Volume	33
Issue number	4
DOIs	https://doi.org/10.4310/CAG.250813161542
Publication status	Published - 27 Aug 2025

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10.4310/CAG.250813161542

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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. This has been reinterpreted geometrically in a number of ways. Here, we give an effective, algorithmic way to construct curves forming a symplectic basis directly from the ideal triangulation of the 3-manifold.",

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AB - 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. This has been reinterpreted geometrically in a number of ways. Here, we give an effective, algorithmic way to construct curves forming a symplectic basis directly from the ideal triangulation of the 3-manifold.

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JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

IS - 4

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A symplectic basis for 3-manifold triangulations

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A symplectic basis for 3-manifold triangulations

Abstract

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