i-manager Publications

An Introduction to Learn Mathematical Knot Theory with Knot Polynomial

D. R. Robert Joan*

Assistant Professor, Department of M.Ed, M.E.T College of Education, Chenbagaramanputhoor, Tamilnadu, India.

Periodicity:April - June'2014
DOI : https://doi.org/10.26634/jmat.3.2.3000

Abstract

In this article, the author discussed the concept of Mathematical Knot Theory and Knot Polynomial. And finally the author collects different knots which are used in the mathematical knot theory. In Mathematics, a knot is an embedding of a 3 circle in 3-dimensional Euclidean space, R , considered up to continuous deformations (isotopies). A crucial difference between the standard mathematical and conventional notions of a knot is that, mathematical knots are closed-there are no ends to tie or untie on a mathematical knot. Physical properties such as friction and thickness also do not apply, although there are mathematical definitions of a knot that take such properties into account. The term knot is also j n applied to embeddings of S in S , especially in the case j= n-2. The branch of Mathematics that studies about knot is known as Knot Theory.

Keywords

Mathematical Knots, Knot Theory, Adding Knot, Prime Knot, Composite Knot, Knot Polynomial.

How to Cite this Article?

Joan, D.R.R. (2014). An Introduction To Learn Mathematical Knot Theory With Knot Polynomial. i-manager’s Journal on Mathematics, 3(2), 7-12. https://doi.org/10.26634/jmat.3.2.3000

References

[1]. Adams, C. C. (1994). The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, pp.280-286.

[2]. Dehn, M. (1914). Die beiden Kleeblattschlingen. Math. Ann, Vol 75, pp.402-413.

[3]. Gordon, C., & Luecke, J. (1989). Knots are Determined by their Complements. Amer. Math. Soc. Vol 2, pp.371-415.

[4]. Hass, J. (1998). Algorithms for recognizing knots and 3-manifolds Chaos, pp.569–581, doi:10.1016/S0960-0779(97)00109- 4.

[5]. Hoste, J. (2005). The enumeration and classification of knots and links. Handbook of Knot Theory.

[6]. Hoste, J., Thistlethwaite, M., & Weeks, J. (1998). The First Knots. Math. Intell, Vol 20, pp.33-48.

[7]. Lickorish, W. B. (1997). An Introduction to Knot Theory. Graduate Texts in Mathematics, Springer-Verlag, ISBN 0-387- 98254-X.

[8]. Livingston, C. (1993). Knot Theory. Washington, DC: Math. Assoc. Amer.

[9]. Rolfsen, D. (1976). Knots and Links, Publish on Perish, ISBN 0-914098-16-0.

[10]. Schubert, H. (1949). Die eindeutige Zerlegbarkeit eines Knotens in Primknoten. Heidelberger Akad. Wiss. Math.-Nat. Kl. Vol 3, pp.57–104.

[11]. Sossinsky, A. (2002). Knots, mathematics with a twist. Harvard University Press, ISBN 0-674-00944-4.

[12]. Thomson, S. W. (1867). On Vortex Atoms, Proceedings of the Royal Society of Edinburgh, pp.94–105.

	North Americas,UK, Middle East,Europe		India	Rest of world
	USD	EUR	INR	USD-ROW
Pdf	35	35	200	20
Online	35	35	200	15
Pdf & Online	35	35	400	25

An Introduction to Learn Mathematical Knot Theory with Knot Polynomial

Abstract

Keywords

How to Cite this Article?

References

If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Options for accessing this content: