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

Joan S. Birman; William W. Menasco

doi:10.1007/s00222-004-0402-3

paper

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

arXiv:math/0407403 · doi:10.1007/s00222-004-0402-3

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 $1 3^{-}$ to $1 1^{-}$ , where we fail to consider the case: $V_{2} = 4, V_{4} > 0, V_{j} = 0$ if $j n o t = 2, 4,$ 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.

6 pages, 4 figures. This is an Erratum to "Studying Links Vai Closed Braids IV: Composite Links and Split Links", Inventiones Math., 102 Facs. 1 (190), 115-139

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