The maximal degree of the Khovanov homology of a cable link

In this paper, we study the Khovanov homology of cable links. We first estimate the maximal homological degree term of the Khovanov homology of the ($2k+1$, $(2k+1)n$)-torus link and give a lower bound of its homological thickness. Specifically, we show that the homological thickness of the ($2k+1$, $(2k+1)n$)-torus link is greater than or equal to $k^{2}n+2$. Next, we study the maximal homological degree of the Khovanov homology of the ($p$, $pn$)-cabling of any knot with sufficiently large $n$. Furthermore, we compute the maximal homological degree term of the Khovanov homology of such a link with even $p$. As an application we compute the Khovanov homology and the Rasmussen invariant of a twisted Whitehead double of any knot with sufficiently many twists.Comment: 40 pages, 26 figures, I shorten some proof

On the Lagrangian fillability of almost positive links

In this paper, we prove that a link which has an almost positive diagram with a certain condition is Lagrangian fillable.Comment: 14 pages, 10 figures, 1 tabl

Realistic description of the rotational bands in rare earth nuclei by angular-momentum-projected multi-cranked configuration-mixing method

Recently we have proposed a reliable method to describe the rotational band in a fully microscopic manner. The method has recourse to the configuration-mixing of several cranked mean-field wave functions after the angular-momentum-projection. By applying the method with the Gogny D1S force as an effective interaction, we investigate the moments of inertia of the ground state rotational bands in a number of selected nuclei in the rare earth region. As another application we try to describe, for the first time, the two-neutron aligned band in $^{164}$Er, which crosses the ground state band and becomes the yrast states at higher spins. Fairly good overall agreements with the experimental data are achieved; for nuclei, where the pairing correlations are properly described, the agreements are excellent. This confirms that the previously proposed method is really useful for study of the nuclear rotational motion