Airi Aso
Published 2020-08-03Version 1
We calculate the twisted Alexander polynomials of all tunnel number one Montesinos knots associated to their $SL_2(\mathbb{C})$-representations and obtain their leading coefficients and degrees. As a corollary, we get some interesting examples, that is, nonfibered knots with monic Alexander polynomials which have non-monic twisted Alexander polynomials.
Comments: 33 pages, 9 figures
Classification of alternating knots with tunnel number one
Tunnel number one, genus one fibered knots
Hyperbolic (1,2)-knots in S^3 with crosscap number two and tunnel number one
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