4 citations · 9 across the 6 of their papers we have counts for
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The ghost character of the (4,5)-torus knot and its applications
Fumikazu Nagasato, Shinnosuke Suzuki
We show that the (4,5)-torus knot admits exactly one ghost character. We then show that this ghost character provides the following two important results. (1) It is known…
Trace-free characters and abelian knot contact homology II
Fumikazu Nagasato, Shinnosuke Suzuki
We show that the - and -torus knots admit ghost characters. Consequently, these knots provide counterexamples to Ng's conjecture, which proposes an isomorphism betwee…
Trace-free characters and abelian knot contact homology I
Fumikazu Nagasato
We study the structure underlying Ng's conjecture, which relates the degree abelian knot contact homology of a knot to the coordinate ring of the -charact…
On minimality of two-bridge knots
Fumikazu Nagasato, Masaaki Suzuki, Anh T. Tran
A knot is called minimal if its knot group admits epimorphisms onto the knot groups of only the trivial knot and itself. In this paper, we determine which two-bridge knot $\mathfra…
Some families of minimal elements for the partial ordering on prime knots
Fumikazu Nagasato, Anh T. Tran
We show that all twist knots, certain double twist knots and some other 2-bridge knots are minimal elements for the partial ordering on the set of prime knots. The key to these res…
On the geometry of the slice of trace--free SL(2,C)-characters of a knot group
Fumikazu Nagasato, Yoshikazu Yamaguchi
Let K be a knot in an integral homology 3-sphere and let B denote the 2-fold branched cover of the integral homology sphere branched along K. We construct a map from the slice of c…
Finiteness of a section of the -character variety of knot groups
Fumikazu Nagasato
We show that for any knot there exist only finitely many irreducible metabelian characters in the -character variety of the knot group, and the number is given ex…