Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
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Finite-volume hyperbolic knot exterior
Definition
For a smooth knot with chosen compact exterior and boundary torus , a finite-volume hyperbolic knot exterior structure is a complete Riemannian metric of constant sectional curvature on with finite volume and exactly one cusp whose torus cross-section is isotopic in to a parallel copy of . The definition asserts no existence.
Depends on
Used by
- Worked case: the figure-eight complement Example
- Baldwin–Sivek instanton-surgery and Newton-polygon input module Lemma
- The standard two-tetrahedron figure-eight gluing is complete Lemma
- Kashaev–Murakami–Murakami volume conjecture for hyperbolic knots Open problem
- Mostow–Prasad rigidity and knot volume Theorem
- Thurston hyperbolization for atoroidal knot exteriors Theorem
Dependency tree · two levels
14 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Jessica S. Purcell, Hyperbolic Knot Theory (standard reference, not scraped)
- William P. Thurston, The Geometry and Topology of Three-Manifolds (standard reference, not scraped)