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On closed $3$-braids

About this Title

Kunio Murasugi

Publication: Memoirs of the American Mathematical Society
Publication Year: 1974; Number 151
ISBNs: 978-0-8218-1851-0 (print); 978-0-8218-9952-6 (online)
DOI: https://doi.org/10.1090/memo/0151
MathSciNet review: 0356023
MSC: Primary 55A25

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Table of Contents

Chapters

  • 1. Terminologies and notations
  • 2. Normal forms
  • 3. Alexander polynomials (I)
  • 4. Alexander polynomials (II)
  • 5. Split links
  • 6. Symmetric polynomials
  • 7. Alexander polynomials (III)
  • 8. Braid index
  • 9. Signature of links (I)
  • 10. Signature of links (II)
  • 11. Signature of links (III)
  • 12. Torus links
  • 13. $\tilde \Omega _{(i)} \cap \tilde \Omega _{(j)}$
  • 14. Classification of link types in $\tilde \Omega _i$ ($i \neq 6$)
  • 15. Link type invariant for $\tilde \Omega _6$
  • 16. Partial classification of link types in $\tilde \Omega _6$
  • 17. Braid index of product links
  • 18. Product links in $\Omega _i$ ($i \neq 6$)
  • 19. Proof of Theorem 17.1 (I)
  • 20. Proof of Theorem 17.1 (II)
  • 21. Proof of Theorem 17.1 (Conclusion)
  • Appendix I. Braid index of classical knots
  • Appendix II. Table of the braid index
  • Appendix III. Braid index of $9_{20}$