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An uncountable collection of arcs in S3 is constructed, each member of which is wild precisely at its endpoints, such that the fundamental groups of their complements are non-trivial, pairwise non-isomorphic, and indecomposable with respect to free products. The fundamental group of the complement of a certain Fox-Artin arc is also shown to be indecomposable.

UNCOUNTABLY MANY ARCS IN S3WHOSE COMPLEMENTS HAVE NON-ISOMORPHIC, INDECOMPOSABLE FUNDAMENTAL GROUPS

UNCOUNTABLY MANY ARCS IN S³WHOSE COMPLEMENTS HAVE NON-ISOMORPHIC, INDECOMPOSABLE FUNDAMENTAL GROUPS