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Article
Upper Bounds for Volumes of Generalized Hyperbolic Polyhedra and Hyperbolic Links
Call a polyhedron in a three-dimensional hyperbolic space generalized if finite, ideal, and truncated vertices are admitted. By Belletti’s theorem of 2021 the exact upper bound for the volumes of generalized h...
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Article
Brieskorn Manifolds, Generalized Sieradski Groups, and Coverings of Lens Spaces
A Brieskorn manifold B(p, q, r) is the r-fold cyclic covering of the 3-sphere S3 branched over the torus knot T(p, q). Generalized Sieradski groups S(m, p, q) are groups with an m-cyclic presentation Gm(w), where...
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Article
Cusped hyperbolic 3-manifolds of complexity 10 having maximum volume
We give a complete census of orientable cusped hyperbolic 3-manifolds obtained by gluing at most ten regular ideal hyperbolic tetrahedra. Although the census is exhaustive, the question of nonhomeomorphism rem...
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Article
Three-dimensional manifolds with poor spines
A special spine of a 3-manifold is said to be poor if it does not contain proper simple subpolyhedra. Using the Turaev-Viro invariants, we establish that every compact 3-manifold M with connected nonempty boundar...
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Article
Two-sided bounds for the complexity of hyperbolic three-manifolds with geodesic boundary
We construct an infinite family of hyperbolic three-manifolds with geodesic boundary that generalize the Thurston and Paoluzzi-Zimmermann manifolds. For the manifolds of this family, we present two-sided bound...
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Article
On Jørgensen numbers and their analogs for groups of figure-eight orbifolds
The Jørgensen, Gehring-Martin-Tan, and Tan numbers are defined for every two-generated subgroup of the group PSL(2,C). These numbers arise in necessary discreteness conditions for two-generated subgroups. The ...
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On the complexity of three-dimensional cusped hyperbolic manifolds
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Article
On complexity of three-dimensional hyperbolic manifolds with geodesic boundary
The nonintersecting classes ℋ p,q are defined, with p, q ∈ ℕ and p ≥ q ≥ 1, of orientable hyperbolic 3-manifolds with geodesic boundary. If M ∈ ℋ p,q ...
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Article
Exact values of complexity for Paoluzzi-Zimmermann manifolds
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Article
Cyclic branched coverings of lens spaces
Some infinite family is constructed of orientable three-dimensional closed manifoldsM n (p, q), where n ≥ 2, p ≥ 3, 0 < q < p, and (p, q) = 1, such that
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Article
Two-sided bounds for the volume of right-angled hyperbolic polyhedra
For a compact right-angled polyhedron R in Lobachevskii space ℍ3, let vol(R) denote its volume and vert(R), the number of its vertices. Upper and lower bounds for vol(R) were recently obtained by Atkinson in term...
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Article
Two-sided complexity bounds for Löbell manifolds
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Article
Surgery on Small Volume Hyperbolic 3-Orbifolds
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Article
Three-dimensional hyperbolic manifolds of small volume with three hyperelliptic involutions
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Article
Spherical coxeter groups and hyperelliptic 3-manifolds
Reflection groups of Coxeter polyhedra in three-dimensional Thurston geometries are examined. For a wide class of Coxeter groups, the existence of subgroups of finite index that uniformize hyperelliptic 3-mani...
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Article
Three-dimensional hyperelliptic manifolds and hamiltonian graphs
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Article
Isometries of hyperbolic Fibonacci manifolds
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Fractional Fibronacci groups and manifolds
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Article
Volumes of hyperbolic Löbell 3-manifolds
In 1931 F. Löbell constructed the first example of a closed orientable three-dimensional hyperbolic manifold. In the present paper we study properties of closed hyperbolic 3-manifolds generalizing Löbell's cla...
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Article
The Heegaard genus of hyperbolic 3-manifolds of small volume