On a conjecture of Dunfield, Friedl and Jackson
Takayuki Morifuji
TL;DR
This paper demonstrates that the twisted Alexander polynomial can detect genus and fibering in twist knots, proving a conjecture for hyperbolic twist knots and advancing understanding of knot invariants.
Contribution
It proves a conjecture by Dunfield, Friedl, and Jackson for hyperbolic twist knots using twisted Alexander polynomials.
Findings
Twisted Alexander polynomial detects genus in twist knots.
It detects fibering in twist knots.
Conjecture of Dunfield, Friedl, and Jackson is confirmed for hyperbolic twist knots.
Abstract
In this short note, we show that the twisted Alexander polynomial associated to a parabolic SL(2,C)-representation detects genus and fibering of the twist knots. As a corollary, a conjecture of Dunfield, Friedl and Jackson is proved for the hyperbolic twist knots.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry