A survey on skein modules via braids

Ioannis Diamantis

A survey on skein modules via braids

Ioannis Diamantis

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

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Abstract

In this paper we present recent results on the computation of skein modules of 3-manifolds using braids and appropriate knot algebras. Skein modules generalize knot polynomials in S^3 to knot polynomials in arbitrary 3-manifolds and they have become extremely essential algebraic tools in the study of 3-manifolds. In this paper we present the braid approach to the HOMFLYPT and the Kauffman bracket skein modules of the Solid Torus ST and the lens spaces L(p,1) and S^1\times S^2.

Original language	English
Title of host publication	Algebraic Structures in Knot Theory
Editors	Carmen Caprau, J. Scott Carter, Neslihan Gügümcü, Sam Nelson
Publisher	American Mathematical Society
Chapter	3
Pages	49-85
Volume	827
ISBN (Print)	978-1-4704-7558-1
Publication status	Published - Dec 2025

Publication series

Series	Contemporary Mathematics
Volume	827

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title = "A survey on skein modules via braids",

abstract = "In this paper we present recent results on the computation of skein modules of 3-manifolds using braids and appropriate knot algebras. Skein modules generalize knot polynomials in S\textasciicircum{}3 to knot polynomials in arbitrary 3-manifolds and they have become extremely essential algebraic tools in the study of 3-manifolds. In this paper we present the braid approach to the HOMFLYPT and the Kauffman bracket skein modules of the Solid Torus ST and the lens spaces L(p,1) and S\textasciicircum{}1\textbackslash{}times S\textasciicircum{}2.",

author = "Ioannis Diamantis",

year = "2025",

month = dec,

language = "English",

isbn = "978-1-4704-7558-1",

volume = "827",

series = "Contemporary Mathematics",

publisher = "American Mathematical Society",

pages = "49--85",

editor = "Carmen Caprau and \{Scott Carter\}, J. and Neslihan G{\"u}g{\"u}mc{\"u} and Sam Nelson",

booktitle = "Algebraic Structures in Knot Theory",

address = "United States",

}

A survey on skein modules via braids. / Diamantis, Ioannis.
Algebraic Structures in Knot Theory. ed. / Carmen Caprau; J. Scott Carter; Neslihan Gügümcü; Sam Nelson. Vol. 827 American Mathematical Society, 2025. p. 49-85 (Contemporary Mathematics, Vol. 827).

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

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AU - Diamantis, Ioannis

PY - 2025/12

Y1 - 2025/12

N2 - In this paper we present recent results on the computation of skein modules of 3-manifolds using braids and appropriate knot algebras. Skein modules generalize knot polynomials in S^3 to knot polynomials in arbitrary 3-manifolds and they have become extremely essential algebraic tools in the study of 3-manifolds. In this paper we present the braid approach to the HOMFLYPT and the Kauffman bracket skein modules of the Solid Torus ST and the lens spaces L(p,1) and S^1\times S^2.

AB - In this paper we present recent results on the computation of skein modules of 3-manifolds using braids and appropriate knot algebras. Skein modules generalize knot polynomials in S^3 to knot polynomials in arbitrary 3-manifolds and they have become extremely essential algebraic tools in the study of 3-manifolds. In this paper we present the braid approach to the HOMFLYPT and the Kauffman bracket skein modules of the Solid Torus ST and the lens spaces L(p,1) and S^1\times S^2.

UR - https://bookstore.ams.org/CONM/827

M3 - Conference article in proceeding

SN - 978-1-4704-7558-1

VL - 827

T3 - Contemporary Mathematics

SP - 49

EP - 85

BT - Algebraic Structures in Knot Theory

A2 - Caprau, Carmen

A2 - Scott Carter, J.

A2 - Gügümcü, Neslihan

A2 - Nelson, Sam

PB - American Mathematical Society

ER -

A survey on skein modules via braids

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