Vol. 45, No. 2, 1973

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Wild arcs in three-space. III. An invariant of oriented local type for exceptional arcs

James Murdoch McPherson

Vol. 45 (1973), No. 2, 599–620

This paper continues the investigations of previous papers in this series, and attention is confined to exceptional arcs. Given a special constructing sequence for an exceptional arc, the associated sequence of local linking matrices is defined, and the cofinality class of this sequence is shown to be an invariant of the oriented local arc type of the exceptional arc. This paper also gives a set of sufficient conditions for an arc to have a constructing sequence.

The paper closes with examples which show that there exist uncountably many locally nonamphicheiral exceptional arcs of any penetration index. No two of the locally nonamphicheiral exceptional arcs exhibited here can be distinguished by the invariant of nonoriented local arc type developed previously.

Mathematical Subject Classification
Primary: 57A10
Secondary: 55A30
Received: 24 November 1971
Published: 1 April 1973
James Murdoch McPherson