Erratum: Studying Links via Closed Braids IV: Composite Links and Split Links
Joan S. Birman, William W. Menasco
Abstract
The purpose of this erratum is to fill a gap in the proof of the `Composite Braid Theorem' in the manuscript "Studying Links Via Closed Braids IV: Composite Links and Split Links (SLVCB-IV)", Inventiones Math, \bf 102\ Fasc. 1 (1990), 115-139. The statement of the theorem is unchanged. The gap occurs on page 135, lines 13- to 11-, where we fail to consider the case: V2 = 4, V4 > 0, Vj=0 if j not= 2,4, and all 4 vertices of valence 2 are bad. At the end of this Erratum we make some brief remarks on the literature, as it has evolved during the 14 years between the publication of SLVCB-IV and the submission of this Erratum.
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