DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedverified 2026-10-22 (gpt-6.1-sol)

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Cyclic cover of zero surgery on a knot

Definition

Assume AC. Let $K$ be a smooth oriented knot and $q \geq 2$ . Let $S_{0}^{3} (K)$ be zero-framed Dehn surgery on $K$ , filling its exterior along the preferred longitude. The exterior meridian-coordinate map to $Z / q$ sends the preferred longitude to zero and therefore extends across this filling. Let $M_{0, q}$ be the connected $q$ -fold cyclic cover classified by its kernel, and let $\tilde{μ}$ denote the closed lift of $μ^{q}$ , where $μ$ is the positive meridian of $K$ .

Definition references

The meridian-mod-q cover convention

The preferred longitude used for zero surgery

Charles Livingston and Swatee Naik, Introduction to Knot Concordance, §7.5.3, p. 139

Existence and uniqueness of the preferred longitude class and the meridian-coordinate map

Extension of the meridian-coordinate map across longitude filling

Axiom of Choice

Depends on

Used by

Dependency tree · two levels

31 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

Anthony Conway, Algebraic Concordance and Casson–Gordon Invariants (standard reference, not scraped)