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

^*Corresponding author for this work

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

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

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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. 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).

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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",

note = "Funding Information: Acknowledgements The author would like to acknowledge several discussions with Professor Sofia Lambropoulou. Moreover, financial support by the China Agricultural University, International College Beijing is gratefully acknowledged. Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2019.",

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",

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}

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

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AU - Diamantis, Ioannis

N1 - Funding Information: Acknowledgements The author would like to acknowledge several discussions with Professor Sofia Lambropoulou. Moreover, financial support by the China Agricultural University, International College Beijing is gratefully acknowledged. Publisher Copyright: © Springer Nature Switzerland AG 2019.

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.

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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

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

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