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We show that under certain considerations the flyping operation on rational tangles, which produces topologically isotopic tangles, may also produce tangles which are not Legendrian isotopic when viewed in the standard contact structure on [special characters omitted]. This work represents an effort to resolve a number of open questions posed by Traynor, by way of techniques inspired by Eliashberg and Fraser. The proofs within employ a new method of diagramming rational tangles which can also be used to easily describe the characteristic foliations of compressing discs for their complements.
| Advisor: | Menasco, William W. |
| Commitee: | Manning, Jason, Sikora, Adam S. |
| School: | State University of New York at Buffalo |
| Department: | Mathematics |
| School Location: | United States -- New York |
| Source: | DAI-B 72/09, Dissertation Abstracts International |
| Source Type: | DISSERTATION |
| Subjects: | Applied Mathematics, Mathematics |
| Keywords: | Characteristic foliation, Compressing discs, Contact geometry, Legendrian tangles, Rational tangles |
| Publication Number: | 3460796 |
| ISBN: | 978-1-124-73181-0 |
