Abstract: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 … Show more
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