English

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

Geometric Topology 2009-11-10 v1 Group Theory

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 1313^- to 1111^-, where we fail to consider the case: V2=4,V4>0,Vj=0V_2 = 4, V_4 > 0, V_j=0 if jnot=2,4,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.

Keywords

Cite

@article{arxiv.math/0407403,
  title  = {Erratum: Studying Links via Closed Braids IV: Composite Links and Split Links},
  author = {Joan S. Birman and William W. Menasco},
  journal= {arXiv preprint arXiv:math/0407403},
  year   = {2009}
}

Comments

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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