An alternative basis for the Kauffman bracket skein module of the Solid Torus via braids

Ioannis Diamantis

doi:10.1007/978-3-030-16031-9_16

An alternative basis for the Kauffman bracket skein module of the Solid Torus via braids

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

Abstract

In this paper we give an alternative basis, \(\mathscr {b}_\mathrm{st}\), for the kauffman bracket skein module of the solid torus, \(\mathrm{kbsm}\left( \mathrm{st}\right) \). The basis \(\mathscr {b}_\mathrm{st}\) is obtained with the use of the tempereley–lieb algebra of type b and it is appropriate for computing the kauffman bracket skein module of the lens spaces l(p, q) via braids.keywordskauffman bracket polynomialskein modulessolid torustemperley–lieb algebra of type bmixed linksmixed braidslens spaces2010 mathematics subject classification57m2757m2520f3620f3820c08.

Original language	English
Title of host publication	Knots, Low-Dimensional Topology and Applications (KNOTS16)
Subtitle of host publication	Knots in Hellas, International Olympic Academy, Greece, July 2016
Editors	Colin C. Adams, Cameron McA. Gordon, Vaughan F.R. Jones, Louis H. Kauffman, Sofia Lambropoulou, Kenneth C. Millett, Jozef H. Przytycki, Renzo Ricca, Radmila Sazdanovic
Publisher	Springer, Cham
Pages	329-345
ISBN (Electronic)	978-3-030-16031-9
ISBN (Print)	978-3-030-16030-2
DOIs	https://doi.org/10.1007/978-3-030-16031-9_16
Publication status	Published - 2019
Externally published	Yes

Publication series

Series	Springer Proceedings in Mathematics and Statistics
Volume	284
ISSN	2194-1009

Access to Document

10.1007/978-3-030-16031-9_16

Cite this

Diamantis, I. (2019). An alternative basis for the Kauffman bracket skein module of the Solid Torus via braids. In C. C. Adams, C. McA. Gordon, V. F. R. Jones, L. H. Kauffman, S. Lambropoulou, K. C. Millett, J. H. Przytycki, R. Ricca, & R. Sazdanovic (Eds.), Knots, Low-Dimensional Topology and Applications (KNOTS16): Knots in Hellas, International Olympic Academy, Greece, July 2016 (pp. 329-345). Springer, Cham. Springer Proceedings in Mathematics and Statistics Vol. 284 https://doi.org/10.1007/978-3-030-16031-9_16

Diamantis, Ioannis. / An alternative basis for the Kauffman bracket skein module of the Solid Torus via braids. Knots, Low-Dimensional Topology and Applications (KNOTS16): Knots in Hellas, International Olympic Academy, Greece, July 2016. editor / Colin C. Adams ; Cameron McA. Gordon ; Vaughan F.R. Jones ; Louis H. Kauffman ; Sofia Lambropoulou ; Kenneth C. Millett ; Jozef H. Przytycki ; Renzo Ricca ; Radmila Sazdanovic. Springer, Cham, 2019. pp. 329-345 (Springer Proceedings in Mathematics and Statistics, Vol. 284).

@inproceedings{37d3c268a7ee4783be4d9015374c9570,

title = "An alternative basis for the Kauffman bracket skein module of the Solid Torus via braids",

abstract = "In this paper we give an alternative basis, \(\mathscr {b}_\mathrm{st}\), for the kauffman bracket skein module of the solid torus, \(\mathrm{kbsm}\left( \mathrm{st}\right) \). The basis \(\mathscr {b}_\mathrm{st}\) is obtained with the use of the tempereley–lieb algebra of type b and it is appropriate for computing the kauffman bracket skein module of the lens spaces l(p, q) via braids.keywordskauffman bracket polynomialskein modulessolid torustemperley–lieb algebra of type bmixed linksmixed braidslens spaces2010 mathematics subject classification57m2757m2520f3620f3820c08.",

author = "Ioannis Diamantis",

year = "2019",

doi = "10.1007/978-3-030-16031-9_16",

language = "English",

isbn = "978-3-030-16030-2",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer, Cham",

pages = "329--345",

editor = "Adams, {Colin C.} and {McA. Gordon}, Cameron and Jones, {Vaughan F.R.} and Kauffman, {Louis H.} and Sofia Lambropoulou and Millett, {Kenneth C.} and Przytycki, {Jozef H.} and Renzo Ricca and Radmila Sazdanovic",

booktitle = "Knots, Low-Dimensional Topology and Applications (KNOTS16)",

address = "Switzerland",

}

Diamantis, I 2019, An alternative basis for the Kauffman bracket skein module of the Solid Torus via braids. in CC Adams, C McA. Gordon, VFR Jones, LH Kauffman, S Lambropoulou, KC Millett, JH Przytycki, R Ricca & R Sazdanovic (eds), Knots, Low-Dimensional Topology and Applications (KNOTS16): Knots in Hellas, International Olympic Academy, Greece, July 2016. Springer, Cham, Springer Proceedings in Mathematics and Statistics, vol. 284, pp. 329-345. https://doi.org/10.1007/978-3-030-16031-9_16

An alternative basis for the Kauffman bracket skein module of the Solid Torus via braids. / Diamantis, Ioannis.

Knots, Low-Dimensional Topology and Applications (KNOTS16): Knots in Hellas, International Olympic Academy, Greece, July 2016. ed. / Colin C. Adams; Cameron McA. Gordon; Vaughan F.R. Jones; Louis H. Kauffman; Sofia Lambropoulou; Kenneth C. Millett; Jozef H. Przytycki; Renzo Ricca; Radmila Sazdanovic. Springer, Cham, 2019. p. 329-345 (Springer Proceedings in Mathematics and Statistics, Vol. 284).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

TY - GEN

T1 - An alternative basis for the Kauffman bracket skein module of the Solid Torus via braids

AU - Diamantis, Ioannis

PY - 2019

Y1 - 2019

N2 - In this paper we give an alternative basis, \(\mathscr {b}_\mathrm{st}\), for the kauffman bracket skein module of the solid torus, \(\mathrm{kbsm}\left( \mathrm{st}\right) \). The basis \(\mathscr {b}_\mathrm{st}\) is obtained with the use of the tempereley–lieb algebra of type b and it is appropriate for computing the kauffman bracket skein module of the lens spaces l(p, q) via braids.keywordskauffman bracket polynomialskein modulessolid torustemperley–lieb algebra of type bmixed linksmixed braidslens spaces2010 mathematics subject classification57m2757m2520f3620f3820c08.

AB - In this paper we give an alternative basis, \(\mathscr {b}_\mathrm{st}\), for the kauffman bracket skein module of the solid torus, \(\mathrm{kbsm}\left( \mathrm{st}\right) \). The basis \(\mathscr {b}_\mathrm{st}\) is obtained with the use of the tempereley–lieb algebra of type b and it is appropriate for computing the kauffman bracket skein module of the lens spaces l(p, q) via braids.keywordskauffman bracket polynomialskein modulessolid torustemperley–lieb algebra of type bmixed linksmixed braidslens spaces2010 mathematics subject classification57m2757m2520f3620f3820c08.

U2 - 10.1007/978-3-030-16031-9_16

DO - 10.1007/978-3-030-16031-9_16

M3 - Conference article in proceeding

SN - 978-3-030-16030-2

T3 - Springer Proceedings in Mathematics and Statistics

SP - 329

EP - 345

BT - Knots, Low-Dimensional Topology and Applications (KNOTS16)

A2 - Adams, Colin C.

A2 - McA. Gordon, Cameron

A2 - Jones, Vaughan F.R.

A2 - Kauffman, Louis H.

A2 - Lambropoulou, Sofia

A2 - Millett, Kenneth C.

A2 - Przytycki, Jozef H.

A2 - Ricca, Renzo

A2 - Sazdanovic, Radmila

PB - Springer, Cham

ER -

Diamantis I. An alternative basis for the Kauffman bracket skein module of the Solid Torus via braids. In Adams CC, McA. Gordon C, Jones VFR, Kauffman LH, Lambropoulou S, Millett KC, Przytycki JH, Ricca R, Sazdanovic R, editors, Knots, Low-Dimensional Topology and Applications (KNOTS16): Knots in Hellas, International Olympic Academy, Greece, July 2016. Springer, Cham. 2019. p. 329-345. (Springer Proceedings in Mathematics and Statistics, Vol. 284). doi: 10.1007/978-3-030-16031-9_16