Erratum: Studying Links via Closed Braids IV: Composite Links and Split Links

Joan S. Birman, William W. Menasco

Published 2004-07-23Version 1

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: $V_2 = 4, V_4 > 0, V_j=0$ 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.