Author:
Haimiao ChenDepartment of Mathematics, Beijing Technology and Business University, 11# Fucheng Road, Haidian District, Beijing, China

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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.

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  • [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.

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  • [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.

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  • [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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2021  
Web of Science  
Total Cites
WoS
589
Journal Impact Factor 0,739
Rank by Impact Factor Mathematics 229/332
Impact Factor
without
Journal Self Cites
0,710
5 Year
Impact Factor
0,654
Journal Citation Indicator 0,57
Rank by Journal Citation Indicator Mathematics 287/474
Scimago  
Scimago
H-index
26
Scimago
Journal Rank
0,265
Scimago Quartile Score Mathematics (miscellaneous) (Q3)
Scopus  
Scopus
Cite Score
1,3
Scopus
CIte Score Rank
General Mathematics 193/391 (Q2)
Scopus
SNIP
0,746

2020  
Total Cites 536
WoS
Journal
Impact Factor
0,855
Rank by Mathematics 189/330 (Q3)
Impact Factor  
Impact Factor 0,826
without
Journal Self Cites
5 Year 1,703
Impact Factor
Journal  0,68
Citation Indicator  
Rank by Journal  Mathematics 230/470 (Q2)
Citation Indicator   
Citable 32
Items
Total 32
Articles
Total 0
Reviews
Scimago 24
H-index
Scimago 0,307
Journal Rank
Scimago Mathematics (miscellaneous) Q3
Quartile Score  
Scopus 139/130=1,1
Scite Score  
Scopus General Mathematics 204/378 (Q3)
Scite Score Rank  
Scopus 1,069
SNIP  
Days from  85
submission  
to acceptance  
Days from  123
acceptance  
to publication  
Acceptance 16%
Rate

2019  
Total Cites
WoS
463
Impact Factor 0,468
Impact Factor
without
Journal Self Cites
0,468
5 Year
Impact Factor
0,413
Immediacy
Index
0,135
Citable
Items
37
Total
Articles
37
Total
Reviews
0
Cited
Half-Life
21,4
Citing
Half-Life
15,5
Eigenfactor
Score
0,00039
Article Influence
Score
0,196
% Articles
in
Citable Items
100,00
Normalized
Eigenfactor
0,04841
Average
IF
Percentile
13,117
Scimago
H-index
23
Scimago
Journal Rank
0,234
Scopus
Scite Score
76/104=0,7
Scopus
Scite Score Rank
General Mathematics 247/368 (Q3)
Scopus
SNIP
0,671
Acceptance
Rate
14%

 

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Studia Scientiarum Mathematicarum Hungarica
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