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.
Zero-framed surgery on a knot
Definition
Assume countable choice as required by the chosen tubular-neighborhood and peripheral-system data. Let K be a smooth oriented knot with compact exterior E_K, positive meridian mu_K, and preferred longitude lambda_K on the boundary torus. The zero-framed surgery manifold M(K) is the closed oriented 3-manifold obtained by gluing D²×S¹ to E_K so that the meridian boundary circle of D²×{1} is identified with lambda_K and a boundary longitude {z₀}×S¹, with z₀∈∂D², is identified with mu_K. This boundary longitude is parallel inside the filling solid torus to its core {0}×S¹. The orientation extends the orientation of E_K across the filling. Thus the filling slope is the preferred zero-linking longitude; the definition asserts no 4-manifold bounded by M(K).
Depends on
Used by
Dependency tree · two levels
6 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
- Tim D. Cochran, Christopher W. Davis, and Arunima Ray, “Injectivity of satellite operators in knot concordance” (standard reference, not scraped)
- Tim D. Cochran, Bridget D. Franklin, Matthew Hedden, and Peter D. Horn, “Knot concordance and homology cobordism” (standard reference, not scraped)