@article{e84eb6c4fb0c443a9406112e88fccb6c,
title = "Twisted alexander polynomials on curves in character varieties of knot groups",
abstract = "For a fibered knot in the 3-sphere the twisted Alexander polynomial associated to an SL(2)-character is known to be monic. It is conjectured that for a nonfibered knot there is a curve component of the SL(2)-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.",
keywords = "57M05, 57M25, Twisted Alexander polynomial, character variety, fibered knot 57M27",
author = "Taehee Kim and Takahiro Kitayama and Takayuki Morifuji",
note = "Funding Information: The authors would like to thank Hiroshi Matsuda for telling us various constructions of closed essential surfaces in knot complements and the literature [7, 29, 30]. They would also like to thank the anonymous referee for helpful comments. The first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Nos. 2012R1A1A001747 and 20120000341). The second author was supported by JSPS Research Fellowships for Young Scientists. The third author was partially supported by Grant-in-Aid for Scientific Research (No. 23540076), the Ministry of Education, Culture, Sports, Science and Technology, Japan.",
year = "2013",
month = mar,
doi = "10.1142/S0129167X13500225",
language = "English",
volume = "24",
journal = "International Journal of Mathematics",
issn = "0129-167X",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "3",
}