2020/11/24 by Anton Mellit, Mellit, Anton
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2011.12279
openalex publication_date 2020/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a compact oriented triangulated 3-manifold we find a non-trivial condition satisfied by certain labelings of the tetrahedra by elements of an arbitrary abelian group which we call angle structures. Smoothness of the manifold is used in an essential way. This is inspired by the notion of the volume of hyperbolic manifolds, which would correspond to the case when the abelian group is the multiplicative group of ℂ, but the construction here seems to be more general, in particular it only uses the abelian group structure.