17 citations · 70 across the 14 of their papers we have counts for
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The equivariant genera of marked strongly invertible knots associated with -bridge knots
Mikami Hirasawa, Ryota Hiura, Makoto Sakuma
A marked strongly invertible knot is a triple of a knot in , a strong inversion of , and a subarc bounded by $\o…
Saddle point braids of braided fibrations and pseudo-fibrations
Benjamin Bode, Mikami Hirasawa
Let be a loop in the space of monic complex polynomials in one variable of fixed degree . If the roots of are distinct for all , they form a braid on st…
Invariant Seifert surfaces for strongly invertible knots
Mikami Hirasawa, Ryota Hiura, Makoto Sakuma
We study invariant Seifert surfaces for strongly invertible knots, and prove that the gap between the equivariant genus (the minimum of the genera of invariant Seifert surfaces) of…
Various stabilities of the Alexander polynomials of knots and links
Mikami Hirasawa, Kunio Murasugi
In this paper, we study distribution of the zeros of the Alexander polynomials of knots and links in S^3. We call a knot or link "real stable" (resp. "circular stable") if all the…
Twisted Alexander polynomials of 2-bridge knots associated to metabelian representations
Mikami Hirasawa, Kunio Murasugi
Suppose the knot group G(K) of a knot K has a non-abelian representation ρon A_4 \subset GL(4,Z). We conjecture that the twisted Alexander polynomial of K associated to ρis of the…
Twisted Alexander polynomials of 2-bridge knots associated to metacyclic representations
Mikami Hirasawa, Kunio Murasugi
Let p be an odd prime and D_p a dihedral group of order 2p. Let ρ: G(K) --> D_p --> GL(p,Z) be a non-abelian representation of the knot group G(K) of a knot K in 3-sphere. Let Δ_{ρ…