Gluing equations for PGL(n,C)-representations of 3-manifolds

Stavros Garoufalidis; Matthias Goerner; Christian K. Zickert

doi:10.2140/agt.2015.15.565

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arXiv · 1207.6711

Gluing equations for PGL(n,C)-representations of 3-manifolds

Stavros Garoufalidis·Matthias Goerner·Christian K. Zickert

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Abstract

In a previous paper, we parametrized boundary-unipotent representations of a 3-manifold group into SL(n,C) using Ptolemy coordinates, which were inspired by A-coordinates on higher Teichmüller space due to Fock and Goncharov. In this paper, we parametrize representations into PGL(n,C) using shape coordinates which are a 3-dimensional analogue of Fock and Goncharov's X-coordinates. These coordinates satisfy equations generalizing Thurston's gluing equations. These equations are of Neumann-Zagier type and satisfy symplectic relations with applications in quantum topology. We also explore a duality between the Ptolemy coordinates and the shape coordinates.

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Stavros Garoufalidis, Matthias Goerner, Christian K. Zickert. 2012-07-28. Gluing equations for PGL(n,C)-representations of 3-manifolds. https://doi.org/10.2140/agt.2015.15.565

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