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 |