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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
Table of Contents
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Front/Back Matter
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