The Algebraic Crossing Number and The Braid Index of Knots and Links
It has been conjectured that the algebraic crossing number of link is uniquely determined in minimal braid representation. This conjecture is true for many classes of knots and links. The Morton-Franks-Williams inequality gives a lower bound for braid index. And sharpness of the inequality on a kno...
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| Định dạng: | Luận án |
| Ngôn ngữ: | en_US |
| Thông tin xuất bản: |
Columbia University
2007
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| Chủ đề: | |
| Truy cập trực tuyến: | http://ir.vnulib.edu.vn/handle/123456789/1377 |
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| Tóm tắt: | It has been conjectured that the algebraic crossing number of link is uniquely determined in minimal braid representation. This conjecture is true for many classes of knots and links.
The Morton-Franks-Williams inequality gives a lower bound for braid index. And sharpness of the inequality on a knot type implies the truth of the conjecture for the knot type.
We prove that there are infinitely many examples of knots and links on which the inequality is not sharp, but the conjecture is still true in these cases.
We also show that if the conjecture is true for K and G, then it is also true for Kp,q, the (p, q)-cable of K, and for K#G, the connect sum of K and G. |
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