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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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Article
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
A Generalization of Fibonacci Groups
We study the class of cyclically presented groups which contain Fibonacci groups and Sieradski groups. Conditions are specified for these groups to be finite, pairwise isomorphic, or aspherical. As a partial a...
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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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Article
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...
