Characterization of 3-bridge links with infinitely many 3-bridge spheres

Abstract

The author, in her previous paper, constructed an infinite family of 3-bridge links each of which admits infinitely many 3-bridge spheres up to isotopy. In this paper, we prove that if a prime, unsplittable link $L$ in $S^3$ admits infinitely many 3-bridge spheres up to isotopy then $L$ belongs to the family.

arXiv comment21 pages, 15 figures