2015/05/21 by Evgeny Fominykh, Fominykh, Evgeny, Vladimir Turaev +3
Mathematics · Physics and Astronomy · #57M20 #57M27 #57M50 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1505.05795
openalex publication_date 2015/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A special spine of a three-manifold is said to be poor if it does not contain proper simple subpolyhedra. Using the Turaev-Viro invariants, we establish that every compact three-dimensional manifold M with connected nonempty boundary has a finite number of poor special spines. Moreover, all poor special spines of the manifold M have the same number of true vertices. We prove that the complexity of a compact hyperbolic three-dimensional manifold with totally geodesic boundary that has a poor special spine with two 2-components and n true vertices is n. Such manifolds are constructed for infinitely many values of n.