THE JONES POLYNOMIAL: A Recurrence Relation Approach

 
9783844311655: THE JONES POLYNOMIAL: A Recurrence Relation Approach

The main problem of knot theory is to differentiate knots. To distinguish knots one needs a knot invariant, which is a function that gives a single value on isotopic knots. The first step toward finding knot invariants was made by Reidemeister by introducing the Reidemeister moves. Even before the discovery of the Reidemeister moves, Alexander defined geometrically a polynomial knot invariant which was later defined by Conway in 1970 in terms of a skein relation. In 1985, V. F. R. Jones revolutionized the knot theory by defining the Jones polynomial as a knot invariant. However, in 1987 L. H. Kauffman introduced a stat-sum model construction of the Jones polynomial that was purely combinatorial and remarkably simple. Our contribution to knot theory includes a general recurrence relation for the Jones polynomial that helps in proving many qualitative results and an expansion formula that drastically reduces the computations in calculating Jones polynomials. We hope this work is not only useful for people who work in classical knot theory but also for people who work in virtual knot theory.

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About the Author:

Dr. Nizami received his PhD in mathematics from Abdus Salam School of Mathematical Sciences, Lahore. His area of interest is knot theory. He is working as assistant professor at University of Education, Lahore.

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Book Description Book Condition: New. Publisher/Verlag: LAP Lambert Academic Publishing | A Recurrence Relation Approach | The main problem of knot theory is to differentiate knots. To distinguish knots one needs a knot invariant, which is a function that gives a single value on isotopic knots. The first step toward finding knot invariants was made by Reidemeister by introducing the Reidemeister moves. Even before the discovery of the Reidemeister moves, Alexander defined geometrically a polynomial knot invariant which was later defined by Conway in 1970 in terms of a skein relation. In 1985, V. F. R. Jones revolutionized the knot theory by defining the Jones polynomial as a knot invariant. However, in 1987 L. H. Kauffman introduced a stat-sum model construction of the Jones polynomial that was purely combinatorial and remarkably simple. Our contribution to knot theory includes a general recurrence relation for the Jones polynomial that helps in proving many qualitative results and an expansion formula that drastically reduces the computations in calculating Jones polynomials. We hope this work is not only useful for people who work in classical knot theory but also for people who work in virtual knot theory. | Format: Paperback | Language/Sprache: english | 68 pp. Bookseller Inventory # K9783844311655

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Book Description LAP Lambert Acad. Publ. Mrz 2011, 2011. Taschenbuch. Book Condition: Neu. Neuware - The main problem of knot theory is to differentiate knots. To distinguish knots one needs a knot invariant, which is a function that gives a single value on isotopic knots. The first step toward finding knot invariants was made by Reidemeister by introducing the Reidemeister moves. Even before the discovery of the Reidemeister moves, Alexander defined geometrically a polynomial knot invariant which was later defined by Conway in 1970 in terms of a skein relation. In 1985, V. F. R. Jones revolutionized the knot theory by defining the Jones polynomial as a knot invariant. However, in 1987 L. H. Kauffman introduced a stat-sum model construction of the Jones polynomial that was purely combinatorial and remarkably simple. Our contribution to knot theory includes a general recurrence relation for the Jones polynomial that helps in proving many qualitative results and an expansion formula that drastically reduces the computations in calculating Jones polynomials. We hope this work is not only useful for people who work in classical knot theory but also for people who work in virtual knot theory. 68 pp. Englisch. Bookseller Inventory # 9783844311655

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Book Description LAP Lambert Acad. Publ. Mrz 2011, 2011. Taschenbuch. Book Condition: Neu. Neuware - The main problem of knot theory is to differentiate knots. To distinguish knots one needs a knot invariant, which is a function that gives a single value on isotopic knots. The first step toward finding knot invariants was made by Reidemeister by introducing the Reidemeister moves. Even before the discovery of the Reidemeister moves, Alexander defined geometrically a polynomial knot invariant which was later defined by Conway in 1970 in terms of a skein relation. In 1985, V. F. R. Jones revolutionized the knot theory by defining the Jones polynomial as a knot invariant. However, in 1987 L. H. Kauffman introduced a stat-sum model construction of the Jones polynomial that was purely combinatorial and remarkably simple. Our contribution to knot theory includes a general recurrence relation for the Jones polynomial that helps in proving many qualitative results and an expansion formula that drastically reduces the computations in calculating Jones polynomials. We hope this work is not only useful for people who work in classical knot theory but also for people who work in virtual knot theory. 68 pp. Englisch. Bookseller Inventory # 9783844311655

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Book Description LAP Lambert Academic Publishing, Germany, 2011. Paperback. Book Condition: New. Language: English . Brand New Book. The main problem of knot theory is to differentiate knots. To distinguish knots one needs a knot invariant, which is a function that gives a single value on isotopic knots. The first step toward finding knot invariants was made by Reidemeister by introducing the Reidemeister moves. Even before the discovery of the Reidemeister moves, Alexander defined geometrically a polynomial knot invariant which was later defined by Conway in 1970 in terms of a skein relation. In 1985, V. F. R. Jones revolutionized the knot theory by defining the Jones polynomial as a knot invariant. However, in 1987 L. H. Kauffman introduced a stat-sum model construction of the Jones polynomial that was purely combinatorial and remarkably simple. Our contribution to knot theory includes a general recurrence relation for the Jones polynomial that helps in proving many qualitative results and an expansion formula that drastically reduces the computations in calculating Jones polynomials. We hope this work is not only useful for people who work in classical knot theory but also for people who work in virtual knot theory. Bookseller Inventory # KNV9783844311655

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Book Description LAP Lambert Acad. Publ. Mrz 2011, 2011. Taschenbuch. Book Condition: Neu. This item is printed on demand - Print on Demand Neuware - The main problem of knot theory is to differentiate knots. To distinguish knots one needs a knot invariant, which is a function that gives a single value on isotopic knots. The first step toward finding knot invariants was made by Reidemeister by introducing the Reidemeister moves. Even before the discovery of the Reidemeister moves, Alexander defined geometrically a polynomial knot invariant which was later defined by Conway in 1970 in terms of a skein relation. In 1985, V. F. R. Jones revolutionized the knot theory by defining the Jones polynomial as a knot invariant. However, in 1987 L. H. Kauffman introduced a stat-sum model construction of the Jones polynomial that was purely combinatorial and remarkably simple. Our contribution to knot theory includes a general recurrence relation for the Jones polynomial that helps in proving many qualitative results and an expansion formula that drastically reduces the computations in calculating Jones polynomials. We hope this work is not only useful for people who work in classical knot theory but also for people who work in virtual knot theory. 68 pp. Englisch. Bookseller Inventory # 9783844311655

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