Vol. 57, No. 1, 1975

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On elementary ideals of projective planes in the 4-sphere and oriented Θ-curves in the 3-sphere

Shin’ichi Kinoshita

Vol. 57 (1975), No. 1, 217–221

The concept of an infinite cyclic covering has been applied to knot theory. In this paper that of a finite cyclic covering is considered. This enable us to study such cases as projective planes in the 4-sphere and oriented 𝜃-curves in the S-sphere. Some properties of elementary ideals of these cases are examined. The technique of free differential calculus is used, instead of that of coverings.

Mathematical Subject Classification
Primary: 57A15
Secondary: 55A25
Received: 16 July 1974
Published: 1 March 1975
Shin’ichi Kinoshita