2016/05/22 by Xavier Morvan, Morvan, Xavier
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT
paper · pdf · doi:10.48550/arxiv.1605.06815
14 pages, 9 figures
arxiv created 2016/05/22 · openalex publication_date 2016/05/22 · arxiv updated 2016/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In his famous Princeton Notes, Thurston introduced the so-called gluing equations defining the deformation variety. Later, Kashaev defined a non-commutative ring from H-triangulations of 3-manifolds and observed that for trefoil and figure-eight knot complements the abelianization of this ring is isomorphic to the ring of regular functions on the deformation variety, \citeKashaev-definitiondeltagroupoid, defanneau, Kashaev-Delta-groupoidsandidealtriangulations. In this paper, we prove that this is true for any knot complement in a homology sphere. We also analyse some examples on other manifolds.