paper

Uncountably many arcs in S^3 whose complements have non-isomorphic, indecomposable fundamental groups

arXiv:math/9901106

Abstract

An uncountable collection of arcs in S^3 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.

17 pages, 16 figures, LaTeX

Uncountably many arcs in S^3 whose complements have non-isomorphic, indecomposable fundamental groups · wovepaper