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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77995An 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, LaTeXGeometric Topology57M30 (Primary) 57N10 (Secondary)Uncountably many arcs in S^3 whose complements have non-isomorphic, indecomposable fundamental groupstext