7 papers · 1 filter
Twisted Alexander vanishing groups of knots
Katsumi Ishikawa, Takayuki Morifuji, Masaaki Suzuki
In our previous work, we introduced the notion of a twisted Alexander vanishing (TAV) group, defined as a finite group for which the corresponding twisted Alexander polynomial of a…
Twisted Alexander polynomials of a knot for group extensions
Katsumi Ishikawa, Takayuki Morifuji, Masaaki Suzuki
In this paper, we discuss twisted Alexander polynomials of a knot for group extensions of a finite group in two directions. Firstly, we provide a mod formula for the twisted Al…
Twisted Alexander vanishing order of knots II
Katsumi Ishikawa, Takayuki Morifuji, Masaaki Suzuki
In our previous work, we introduced the notion of the twisted Alexander vanishing order of knots, defined as the order of the smallest finite group for which the corresponding twis…
Torsion elements in the associated graded of the -filtration of the monoid of homology cylinders
Yuta Nozaki, Masatoshi Sato, Masaaki Suzuki
Clasper surgery induces the -filtration over the monoid of homology cylinders, which serves as a -dimensional analogue of the lower central series of…
Twisted Alexander polynomials of knots associated to the regular representations of finite groups
Takayuki Morifuji, Masaaki Suzuki
The twisted Alexander polynomial of a knot is defined associated to a linear representation of the knot group. If there exists a surjective homomorphism of a knot group onto a fini…
On the braid index of a two-bridge knot
Masaaki Suzuki, Anh T. Tran
In this paper, we consider two properties on the braid index of a two-bridge knot. We prove an inequality on the braid indices of two-bridge knots if there exists an epimorphism be…