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- W2066039145 abstract "In this paper we consider free actions of finite cyclic groups on the pair ( S 3 , K ), where K is a knot in S 3 . That is, we look at periodic diffeo-morphisms f of ( S 3 , K ) such that f n is fixed point free, for all n less than the order of f . Note that such actions are always orientation preserving. We will show that if K is a non-trivial prime knot then, up to conjugacy, ( S 3 , K ) has at most one free finite cyclic group action of a given order. In addition, if all of the companions of K are prime, then all of the free periodic diffeo-morphisms of ( S 3 , K ) are conjugate to elements of one cyclic group which acts freely on ( S 3 , K ). More specifically, we prove the following two theorems. THEOREM 1. Let K be a non-trivial prime knot. If f and g are free periodic diffeomorphisms of (S 3 , K) of the same order, then f is conjugate to a power of g." @default.
- W2066039145 created "2016-06-24" @default.
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- W2066039145 date "1987-08-01" @default.
- W2066039145 modified "2023-10-04" @default.
- W2066039145 title "Uniqueness of Free Actions on S3 Respecting a Knot" @default.
- W2066039145 doi "https://doi.org/10.4153/cjm-1987-049-3" @default.
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