Standard
Extending the Classical Skein. / Kauffman, Louis H.; Lambropoulou, Sofia.
Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016. ed. / Colin C. Adams; Cameron McA. Gordon; Vaughan F.R. Jones; Louis H. Kauffman; Sofia Lambropoulou; Kenneth C. Millett; Jozef H. Przytycki; Jozef H. Przytycki; Renzo Ricca; Radmila Sazdanovic. Springer New York LLC, 2019. p. 225-245 (Springer Proceedings in Mathematics and Statistics; Vol. 284).
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
Harvard
Kauffman, LH & Lambropoulou, S 2019,
Extending the Classical Skein. in CC Adams, CM Gordon, VFR Jones, LH Kauffman, S Lambropoulou, KC Millett, JH Przytycki, JH Przytycki, R Ricca & R Sazdanovic (eds),
Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016. Springer Proceedings in Mathematics and Statistics, vol. 284, Springer New York LLC, pp. 225-245, International Olympic Academy, 2016, Ancient Olympia, Greece,
17.07.2016.
https://doi.org/10.1007/978-3-030-16031-9_11APA
Kauffman, L. H., & Lambropoulou, S. (2019).
Extending the Classical Skein. In C. C. Adams, C. M. Gordon, V. F. R. Jones, L. H. Kauffman, S. Lambropoulou, K. C. Millett, J. H. Przytycki, J. H. Przytycki, R. Ricca, & R. Sazdanovic (Eds.),
Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016 (pp. 225-245). (Springer Proceedings in Mathematics and Statistics; Vol. 284). Springer New York LLC.
https://doi.org/10.1007/978-3-030-16031-9_11Vancouver
Kauffman LH, Lambropoulou S.
Extending the Classical Skein. In Adams CC, Gordon CM, Jones VFR, Kauffman LH, Lambropoulou S, Millett KC, Przytycki JH, Przytycki JH, Ricca R, Sazdanovic R, editors, Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016. Springer New York LLC. 2019. p. 225-245. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-030-16031-9_11
Author
Kauffman, Louis H. ; Lambropoulou, Sofia. /
Extending the Classical Skein. Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016. editor / Colin C. Adams ; Cameron McA. Gordon ; Vaughan F.R. Jones ; Louis H. Kauffman ; Sofia Lambropoulou ; Kenneth C. Millett ; Jozef H. Przytycki ; Jozef H. Przytycki ; Renzo Ricca ; Radmila Sazdanovic. Springer New York LLC, 2019. pp. 225-245 (Springer Proceedings in Mathematics and Statistics).
BibTeX
@inproceedings{77b470a4b88b48babf55c310416b4054,
title = "Extending the Classical Skein",
abstract = "We summarize the theory of a new skein invariant of classical links H[H] that generalizes the regular isotopy version of the Homflypt polynomial, H. The invariant H[H] is based on a procedure where we apply the skein relation only to crossings of distinct components, so as to produce collections of unlinked knots and then we evaluate the resulting knots using the invariant H and inserting at the same time a new parameter. This procedure, remarkably, leads to a generalization of H but also to generalizations of other known skein invariants, such as the Kauffman polynomial. We discuss the different approaches to the link invariant H[H], the algebraic one related to its ambient isotopy equivalent invariant, the skein-theoretic one and its reformulation into a summation of the generating invariant H on sublinks of a given link. We finally give examples illustrating the behaviour of the invariant H[H] and we discuss further research directions and possible application areas.",
keywords = "3-variable link invariant, Classical links, Closed combinatorial formulae, Dubrovnik polynomial, Homflypt polynomial, Kauffman polynomial, Mixed crossings, Reidemeister moves, Skein invariants, Skein relations, Stacks of knots, Yokonuma–Hecke algebras",
author = "Kauffman, {Louis H.} and Sofia Lambropoulou",
year = "2019",
month = jan,
day = "1",
doi = "10.1007/978-3-030-16031-9_11",
language = "English",
isbn = "9783030160302",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer New York LLC",
pages = "225--245",
editor = "Adams, {Colin C.} and Gordon, {Cameron McA.} and Jones, {Vaughan F.R.} and Kauffman, {Louis H.} and Sofia Lambropoulou and Millett, {Kenneth C.} and Przytycki, {Jozef H.} and Przytycki, {Jozef H.} and Renzo Ricca and Radmila Sazdanovic",
booktitle = "Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016",
address = "United States",
note = "International Olympic Academy, 2016 ; Conference date: 17-07-2016 Through 23-07-2016",
}
RIS
TY - GEN
T1 - Extending the Classical Skein
AU - Kauffman, Louis H.
AU - Lambropoulou, Sofia
PY - 2019/1/1
Y1 - 2019/1/1
N2 - We summarize the theory of a new skein invariant of classical links H[H] that generalizes the regular isotopy version of the Homflypt polynomial, H. The invariant H[H] is based on a procedure where we apply the skein relation only to crossings of distinct components, so as to produce collections of unlinked knots and then we evaluate the resulting knots using the invariant H and inserting at the same time a new parameter. This procedure, remarkably, leads to a generalization of H but also to generalizations of other known skein invariants, such as the Kauffman polynomial. We discuss the different approaches to the link invariant H[H], the algebraic one related to its ambient isotopy equivalent invariant, the skein-theoretic one and its reformulation into a summation of the generating invariant H on sublinks of a given link. We finally give examples illustrating the behaviour of the invariant H[H] and we discuss further research directions and possible application areas.
AB - We summarize the theory of a new skein invariant of classical links H[H] that generalizes the regular isotopy version of the Homflypt polynomial, H. The invariant H[H] is based on a procedure where we apply the skein relation only to crossings of distinct components, so as to produce collections of unlinked knots and then we evaluate the resulting knots using the invariant H and inserting at the same time a new parameter. This procedure, remarkably, leads to a generalization of H but also to generalizations of other known skein invariants, such as the Kauffman polynomial. We discuss the different approaches to the link invariant H[H], the algebraic one related to its ambient isotopy equivalent invariant, the skein-theoretic one and its reformulation into a summation of the generating invariant H on sublinks of a given link. We finally give examples illustrating the behaviour of the invariant H[H] and we discuss further research directions and possible application areas.
KW - 3-variable link invariant
KW - Classical links
KW - Closed combinatorial formulae
KW - Dubrovnik polynomial
KW - Homflypt polynomial
KW - Kauffman polynomial
KW - Mixed crossings
KW - Reidemeister moves
KW - Skein invariants
KW - Skein relations
KW - Stacks of knots
KW - Yokonuma–Hecke algebras
UR - http://www.scopus.com/inward/record.url?scp=85069194716&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-16031-9_11
DO - 10.1007/978-3-030-16031-9_11
M3 - Conference contribution
AN - SCOPUS:85069194716
SN - 9783030160302
T3 - Springer Proceedings in Mathematics and Statistics
SP - 225
EP - 245
BT - Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016
A2 - Adams, Colin C.
A2 - Gordon, Cameron McA.
A2 - Jones, Vaughan F.R.
A2 - Kauffman, Louis H.
A2 - Lambropoulou, Sofia
A2 - Millett, Kenneth C.
A2 - Przytycki, Jozef H.
A2 - Przytycki, Jozef H.
A2 - Ricca, Renzo
A2 - Sazdanovic, Radmila
PB - Springer New York LLC
T2 - International Olympic Academy, 2016
Y2 - 17 July 2016 through 23 July 2016
ER -
