arXiv subjects

Shinnosuke Suzuki

Publications and source records attributed to Shinnosuke Suzuki.

3 recordsLinked to original sources

arXiv2017

Trace-free characters and abelian knot contact homology II

We show that the $(4,5)$- and $(5,6)$-torus knots admit ghost characters. Consequently, these knots provide counterexamples to Ng's conjecture, which proposes an isomorphism between the complexification of degree $0$ abelian knot contact homology and the coordinate ring of the character variety of the $2$-fold branched cover of the $3$-sphere branched along a knot. While Ng's conjecture has been verified for all $2$-bridge and $3$-bridge knots, we demonstrate, via ghost characters, how this isomorphism fails for these torus knots.

math.GT↗

arXiv2017

The ghost character of the (4,5)-torus knot and its applications

We show that the (4,5)-torus knot $T_{4,5}$ admits exactly one ghost character. We then show that this ghost character provides the following two important results. (1) It is known that for any knot $K$ every (meridionally) trace-free $\SL_2(\C)$-representation of the knot group $G(K)$ yields an $\SL_2(\C)$-representation of the fundamental group $\pi_1(\Sigma_2K)$ of the 2-fold branched cover $\Sigma_2K$ of the 3-sphere along $K$. This correspondence often but not always provides all $\SL_2(\C)$-representations of $\pi_1(\Sigma_2K)$. We show by using the ghost character that $T_{4,5}$ is the simplest torus knot such that $\pi_1(\Sigma_2T_{4,5})$ admits an $\SL_2(\C)$-representation which cannot be realized by any trace-free $\SL_2(\C)$-representations. (2) We show that $T_{4,5}$ is the simplest torus knot that provides a counterexample to Ng's conjecture, concerned with a polynomial map $h^*$ between the character variety $X(\Sigma_2K)$ of $\pi_1(\Sigma_2K)$ and the fundamental variety $F_2(K)$. More precisely, the map $h^*$ is surjective but not injective, and hence not an isomorphism for $T_{4,5}$.

math.GT↗

arXiv2013

Two Fermi surface states and two $T_{\rm c}$-rising mechanisms revealed by transport properties in $R$FeP$_{1-x}$As$_x$O$_{0.9}$F$_{0.1}$ ($R$=La, Pr and Nd)

We demonstrate the relation between critical temperature $T_{\rm c}$ and transport properties in $R$FeP$_{1-x}$As$_x$O$_{0.9}$F$_{0.1}$ ($R$=La, Pr and Nd). $T_{\rm c}$ and resistivity power-law exponent $n$ form a universal line on the $T_{\rm c}$ vs. $n$ plane for all the $R$-systems with $x$$<0.6\sim$0.8, indicating that $T_{\rm c}$ increases with bosonic fluctuation. Transport properties show anomalies suggesting a change of Fermi surfaces around $x$=0.6$\sim$0.8. Above $x$=0.6$\sim$0.8, $T_{\rm c}$ and $n$ approach the second $T_{\rm c}$-$n$ line for the higher $T_{\rm c}$ systems. A further increase of $T_{\rm c}$ above $x$=0.6$\sim$0.8 indicates the presence of an additional $T_{\rm c}$-rising mechanism in this system.

cond-mat.supr-con↗