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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- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
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These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Lens spaces in the filling orientation convention
Definition
Assume . An oriented lens space is an oriented closed -manifold obtained by gluing two solid tori by an orientation-reversing boundary homeomorphism. For coprime integers and , let denote the oriented union of the exterior of the unknot in the oriented -sphere and a solid torus whose meridian is identified with the slope on the unknot exterior. Thus this library uses the convention ; no symbol is assigned.
Depends on
Used by
- Worked cases of Dehn surgery on the unknot Example
- Worked cases of three-manifold surgery presentations Example
- A rational homology ball bounded by L(4,1) Lemma
- Lens-space correction-term formula for L(p,1) Lemma
- The genus-one hat Floer complex of an order-three lens space has rank three Lemma
- The trefoil double branched cover is a lens space of order three Lemma
Dependency tree · two levels
10 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
- Nikolai Saveliev, Lectures on the Topology of 3-Manifolds, 2nd revised edition, Lecture 1 §1.5 and Lecture 2 §2.3 (standard reference, not scraped)
- Peter S. Ozsváth, András I. Stipsicz, and Zoltán Szabó, Heegaard Floer homology, version 2025-12-15, Exercise 1.2.14(b) (standard reference, not scraped)