On universal groups and three-manifolds

DOI10.1007/BF01389236zbMath0613.57007OpenAlexW2025407840MaRDI QIDQ1819417

Hugh M. Hilden, Wilbur Whitten, José María Montesinos Amilibia

Publication date: 1987

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143429

zbMATH Keywords

3-manifoldhyperbolic 3-spacehyperbolic orbifoldPoincaré conjecture\(PSL_ 2({bbfC})\)covering branched over the Borromean ringsregular dodecahedron

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Low-dimensional topology of special (e.g., branched) coverings (57M12)

Related Items

Cone 3-Manifolds, On the Borromean arithmetic orbifolds, Telescopic actions, Harmonic manifolds and embedded surfaces arising from a super regular tesselation, \(H^3\) as a harmonic branched covering of \(E^3\), Universal presentations for manifold groups, Finite group actions on handlebodies and equivariant Heegaard genus for 3-manifolds, Universal coverings of PL-manifolds via coloured graphs, On three-fold irregular branched coverings over closed three-braid and three-bridge knots, ON UNIVERSAL KLEINIAN GROUPS GENERATED BY 180° ROTATIONS, Virtual domination of 3-manifolds, A Survey of the Impact of Thurston’s Work on Knot Theory, Universal quantum computing and three-manifolds

Cites Work

• The Whitehead link, the Borromean rings and the knot \(9_{46}\) are universal
• On knots that are universal
• A representation of closed, orientable 3-manifolds as 3-fold branched coverings of 𝑆³
• Every closed orientable 3-manifold is a 3-fold branched covering space of $S^3$
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