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

Robert Myers

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arXiv · math/9901106

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

Robert Myers

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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.

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Robert Myers. 1999-01-25. Uncountably many arcs in S^3 whose complements have non-isomorphic, indecomposable fundamental groups. https://arxiv.org/abs/math/9901106

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