5 papers
-knots with the same knot group but different knot quandles
Kokoro Tanaka, Yuta Taniguchi
We give a first example of 2-knots with the same knot group but different knot quandles by analyzing the knot quandles of twist spins. As a byproduct of the analysis, we also give…
Twisted Alexander matrices of quandles associated with a certain Alexander pair
Yuta Taniguchi
Ishii and Oshiro introduced the notion of an -twisted Alexander matrix, which is a quandle version of a twisted Alexander matrix and defined an invariant of finitely presented q…
Good involutions of generalized Alexander quandles
Yuta Taniguchi
Quandles with good involutions, which are called symmetric quandles, can be used to define invariants of unoriented knots and links. In this paper, we determine the necessary and s…
A homogeneous presentation of symmetric quandles
Yuta Taniguchi
A quandle is an algebraic structure whose axioms correspond to the Reidemeister moves of knot theory. S. Kamada introduced the notion of a quandle with a good involution, which is…
Alexander matrices of link quandles associated to quandle homomorphisms and quandle cocycle invariants
Yuta Taniguchi
A. Ishii and K. Oshiro introduced the notion of an -twisted Alexander matrix. This notion is a quandle version of the twisted Alexander matrix which was introduced by M. Wada. T…