arXiv subjects

Norihisa Takahashi

Publications and source records attributed to Norihisa Takahashi.

3 recordsLinked to original sources

arXiv2026

HOMFLY Polynomials of the Torus Links

We derive explicit formulas for the HOMFLY polynomials of the torus links $T(3,n)$ using braid groups and the skein relation. We first treat the case of $T(2,n)$ and then derive a five-term linear recurrence for an auxiliary sequence associated with $T(3,n)$. By solving this recurrence using a generating function, we obtain an explicit formula for the HOMFLY polynomial $P(T(3,n);y,z)$ of $T(3,n)$. The corresponding formula for $T(-3,n)$ is subsequently obtained from the mirror-image formula for the HOMFLY polynomial. As an application, we show that the HOMFLY polynomial distinguishes the links $T(3,n)$ within this family and distinguishes $T(3,n)$ from its mirror image for $n\geq 2$.

math.GT↗

arXiv2025

On a classification of irreducible periodic diffeomorphisms on surfaces which commute with certain involution

Ishizaka classified up to conjugacy hyperelliptic periodic automorphisms of a surface. Here, an involution $I$ on a surface $Σ_{g}$ is hyperelliptic if and only if $Σ_{g}/\langle I \rangle$ is homeomorphic to $S^2$. In this article, we give a classification up to conjugacy for irreducible periodic automorphisms of a surface $Σ_{g}$ which commute with involutions $ι$ such that $Σ_{g}/\langle ι\rangle$ is homeomorphic to $T^{2}$.

math.AT↗

arXiv2019

Dehn twist presentations of hyperelliptic periodic diffeomorphisms on closed surfaces

We classify up to conjugacy the group generated by a commuting pair of a periodic diffeomorphism and a hyperelliptic involution on an oriented closed surface. This result can be viewed as a refinement of Ishizaka's result on classification of the mapping classes of hyperelliptic periodic diffeomorphisms. As an application, we obtain the Dehn twist presentations of hyperelliptic periodic mapping classes, which are closely related to the ones obtained by Ishizaka.

math.GT↗