A symplectic basis for 3-manifold triangulations

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Mathews, Daniel V., Purcell, Jessica S.
Format: Preprint
Published: 2022
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866918132189233152
author Mathews, Daniel V.
Purcell, Jessica S.
author_facet Mathews, Daniel V.
Purcell, Jessica S.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2208_06969
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle A symplectic basis for 3-manifold triangulations
Mathews, Daniel V.
Purcell, Jessica S.
Geometric Topology
57K30, 57K31
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.
title A symplectic basis for 3-manifold triangulations
topic Geometric Topology
57K30, 57K31
url https://arxiv.org/abs/2208.06969