Finiteness theorems for conjugacy classes and branched covers of knots (Q1263132)

This paper contains some finiteness results concerning high dimensional knots. An n-knot k is a PL oriented pair \((S^{n+2},S^ n)\). It is shown that if k is a stable knot or a simple 3-knot, then k is determined up to finite ambiguity by its knot modules. For a given positive integer r, a stable knot (or a simple 3-knot) can be the r-fold branched cyclic cover of at most finitely many knots. The operation of p-spinning, which takes stable n-knots to stable \((n+p)\)-knots, is finite to one.