Divisibility of the Conway polynomial of links
| dc.contributor.advisor | Cochran, Tim D. | en_US |
| dc.creator | Lampazzi, Amy M. Noel | en_US |
| dc.date.accessioned | 2009-06-04T06:43:44Z | en_US |
| dc.date.available | 2009-06-04T06:43:44Z | en_US |
| dc.date.issued | 2001 | en_US |
| dc.description.abstract | The Conway polynomial ∇K = c0 + c1z + c2z2...of a link K is an invariant of links. In this paper we extend a theorem of J. Levine [5] regarding divisibility of the Conway polynomial by monomials of the form zi. Three different definitions of finite type invariants of links are presented, including a definition of surgery finite type. When the coefficients ci are considered as finite type invariants, the type of these invariants is closely related to the degree of the monomials which can be factored out of ∇K. With this in mind, we prove an extension of a conjecture by T. Cochran and P. Melvin [2] concerning the divisibility of an alternating sum sum S<L ∇K(Sigma S) of Conway polynomials of an algebraically split link K in various surgered spheres. This result was also proved for a more general case in which the link K is not necessarily algebraically split. Finally, corollaries relate these theorems to the type of the coefficients ci, considered as finite type invariants. | en_US |
| dc.format.extent | 28 p. | en_US |
| dc.format.mimetype | application/pdf | en_US |
| dc.identifier.callno | THESIS MATH. 2001 LAMPAZZI | en_US |
| dc.identifier.citation | Lampazzi, Amy M. Noel. "Divisibility of the Conway polynomial of links." (2001) Diss., Rice University. <a href="https://hdl.handle.net/1911/17995">https://hdl.handle.net/1911/17995</a>. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/17995 | en_US |
| dc.language.iso | eng | en_US |
| dc.rights | Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. | en_US |
| dc.subject | Mathematics | en_US |
| dc.title | Divisibility of the Conway polynomial of links | en_US |
| dc.type | Thesis | en_US |
| dc.type.material | Text | en_US |
| thesis.degree.department | Mathematics | en_US |
| thesis.degree.discipline | Natural Sciences | en_US |
| thesis.degree.grantor | Rice University | en_US |
| thesis.degree.level | Doctoral | en_US |
| thesis.degree.name | Doctor of Philosophy | en_US |
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