TWISTED ALEXANDER POLYNOMIALS ON CURVES IN CHARACTER VARIETIES OF KNOT GROUPS
2013 ◽
Vol 24
(03)
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pp. 1350022
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Keyword(s):
For a fibered knot in the 3-sphere the twisted Alexander polynomial associated to an SL(2, ℂ)-character is known to be monic. It is conjectured that for a nonfibered knot there is a curve component of the SL(2, ℂ)-character variety containing only finitely many characters whose twisted Alexander polynomials are monic, i.e. finiteness of such characters detects fiberedness of knots. In this paper, we discuss the existence of a certain curve component which relates to the conjecture when knots have nonmonic Alexander polynomials. We also discuss the similar problem of detecting the knot genus.
2012 ◽
Vol 23
(06)
◽
pp. 1250022
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2020 ◽
Vol 29
(04)
◽
pp. 2050016
2013 ◽
Vol 156
(1)
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pp. 81-97
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Keyword(s):
2013 ◽
Vol 22
(01)
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pp. 1250138
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Keyword(s):
2016 ◽
Vol 25
(11)
◽
pp. 1650065
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2018 ◽
Vol 27
(02)
◽
pp. 1850015
◽
2018 ◽
Vol 27
(04)
◽
pp. 1850026
2010 ◽
Vol 19
(10)
◽
pp. 1355-1400
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2018 ◽
Vol 70
(2)
◽
pp. 354-399
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