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Spaces of polynomial knots in low degree

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dc.contributor.author MISHRA, RAMA en_US
dc.contributor.author RAUNDAL, HITESH en_US
dc.date.accessioned 2022-06-24T10:42:13Z
dc.date.available 2022-06-24T10:42:13Z
dc.date.issued 2015-01 en_US
dc.identifier.citation Journal of Knot Theory and Its Ramifications, 24(14), 1550073. en_US
dc.identifier.issn 0218-2165 en_US
dc.identifier.issn 1793-6527 en_US
dc.identifier.uri https://doi.org/10.1142/S021821651550073X en_US
dc.identifier.uri http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/7193
dc.description.abstract We show that all knots up to six crossings can be represented by polynomial knots of degree at most 7, among which except for 52,5∗2,61,6∗1,62,6∗2 and 63 all are in their minimal degree representation. We provide concrete polynomial representation of all these knots. Durfee and O’Shea had asked a question: Is there any 5-crossing knot in degree 6? In this paper we try to partially answer this question. For an integer d≥2, we define a set P˜d to be the set of all polynomial knots given by t↦(f(t),g(t),h(t)) such that deg(f)=d−2,deg(g)=d−1 and deg(h)=d. This set can be identified with a subset of R3d and thus it is equipped with the natural topology which comes from the usual topology R3d. In this paper we determine a lower bound on the number of path components of P˜d for d≤7. We define a path equivalence for polynomial knots in the space P˜d and show that it is stronger than the topological equivalence. en_US
dc.language.iso en en_US
dc.publisher World Scientific Publishing en_US
dc.subject Polynomial knot en_US
dc.subject Polynomial representation of a knot en_US
dc.subject Polynomial degree of a knot en_US
dc.subject Spaces of polynomial knots en_US
dc.subject Path equivalence en_US
dc.subject 2015 en_US
dc.title Spaces of polynomial knots in low degree en_US
dc.type Article en_US
dc.contributor.department Dept. of Mathematics en_US
dc.identifier.sourcetitle Journal of Knot Theory and Its Ramifications en_US
dc.publication.originofpublisher Foreign en_US


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