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Braid and Knot Theory in Dimension Four

About this Title

Seiichi Kamada, Osaka City University, Osaka, Japan

Publication: Mathematical Surveys and Monographs
Publication Year: 2002; Volume 95
ISBNs: 978-0-8218-2969-1 (print); 978-1-4704-1322-4 (online)
DOI: https://doi.org/10.1090/surv/095
MathSciNet review: MR1900979
MSC: Primary 57Q45; Secondary 20F36, 57M25, 57Q35

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Table of Contents

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Front/Back Matter

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Chapters

• 0. Basic notions and notation
• 1. Braids
• 2. Braid automorphisms
• 3. Classical links
• 4. Braid presentation of links
• 5. Deformation chain and Markov’s theorem
• 6. Surface links
• 7. Surface link diagrams
• 8. Motion pictures
• 9. Normal forms of surface links
• 10. Examples (spinning)
• 11. Ribbon surface links
• 12. Presentations of surface link groups
• 13. Branched coverings
• 14. Surface braids
• 15. Products of surface braids
• 16. Braided surfaces
• 17. Braid monodromy
• 18. Chart descriptions
• 19. Non-simple surface braids
• 20. 1-Handle surgery on surface braids
• 21. The normal braid presentation
• 22. Braiding ribbon surface links
• 23. Alexander’s theorem in dimension four
• 24. Split union and connected sum
• 25. Markov’s theorem in dimension four
• 26. Proof of Markov’s theorem in dimension four
• 27. Knot groups
• 28. Unknotted surface braids and surface links
• 29. Ribbon surface braids and surface links
• 30. 3-Braid 2-knots
• 31. Unknotting surface braids and surface links
• 32. Seifert algorithm for surface braids
• 33. Basic symmetries in chart descriptions
• 34. Singular surface braids and surface links