Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 59: Issue 1
The Sl(2, )-Character Variety of a Montesinos Knot
Author:
Haimiao Chen Department of Mathematics, Beijing Technology and Business University, 11# Fucheng Road, Haidian District, Beijing, China

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Pages:
75–91
Online Publication Date:
01 Apr 2022
Publication Date:
01 Apr 2022
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2022.01519
Keywords:
SL(2, C)-character variety; irreducible representation; Montesinos knot; rational tangle
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For each Montesinos knot K, we propose an efficient method to explicitly determine the irreducible SL(2, )-character variety, and show that it can be decomposed as χ0(K)⊔χ1(K)⊔χ2(K)⊔χ'(K), where χ0(K) consists of trace-free characters χ1(K) consists of characters of “unions” of representations of rational knots (or rational link, which appears at most once), χ2(K) is an algebraic curve, and χ'(K) consists of finitely many points when K satisfies a generic condition.

  • [1]

    C. Ashley, J.-P. Burelle and S. Lawton. Rank 1 character varieties of finitely presented groups. Geom. Dedicata 192:1-19, 2018.

  • [2]

    H.-M. Chen. Trace-free SL(2, )-representations of Montesinos links. J. Knot Theor Ramif 27(8):1850050, 2018.

  • [3]

    H.-M. Chen. Character varieties of odd classical pretzel knots. Int. J. Math. 29(9):1850060, 2018.

  • [4]

    H.-M. Chen. Character varieties of even classical pretzel knots. Stud. Sci. Math. Hung. 56(4):510-522, 2019.

  • [5]

    M. Culler and N. Dunfeld. Orderability and Dehn filling. Geom. Topol. 22(3):1405-1457, 2018.

  • [6]

    M. Culler and P.B. Shalen, Varieties of group representations and splittings of 3-manifolds. Ann. Math. (2) 117(1):109-146, 1983.

  • [7]

    S. Friedl and S. Vidussi. A survey of twisted Alexander polynomials. In M. Banagl and D. Vogel, editors, The mathematics of knots, Springer-Verlag Berlin Heidelberg, 2011.

    • Search Google Scholar
    • Export Citation
  • [8]

    K. Ichihara and I.D. Jong. Seifert fibered surgery and Rasmussen invariant. Contemp. Math. 597:321-336, 2013.

  • [9]

    A. Khan and AT. Tran. Classical pretzel knots and left orderability. Int. J. Math. 32(11):2150080, 2021.

  • [10]

    M. L. Macasieb, K. L. Petersen and R. van Luijk. On character varieties of two-bridge knot groups. Proc. Lond. Math. Soc. 103(3):473-507, 2011.

    • Search Google Scholar
    • Export Citation
  • [11]

    V. Muñoz. The SL(2, )-character varieties of torus knots. Revista Mate. Compl. 22(2):489-497, 2009.

  • [12]

    L. Paoluzzi and J. Porti. Non-standard components of the character variety for a family of Montesinos knots. Proc. Lond. Math. Soc. 107(3):655-679, 2013.

    • Search Google Scholar
    • Export Citation
  • [13]

    K. L. Petersen and A. T. Tran. Character varieties of double twist links. Algebraic Geom. Topol. 15:3569-3598, 2015.

  • [14]

    R. Riley. Nonabelian representations of 2-bridge knot groups. Quart. J. Math. Oxford Ser. (2), 35(138):191-208, 1984.

  • [15]

    A. T. Tran. Character varieties of (-2, 2m+1, 2n)-pretzellinks and twisted Whitehead links. J. Knot. Theor. Ramif. 25(2):1650007 2016.

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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

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Gábor SÁGI (Rényi Institute of Mathematics)

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  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation		 1966
Volumes
per Year		 1
Issues
per Year		 4
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
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ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

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