Unknotting numbers and triple point cancelling numbers of torus-covering knots

It is known that any surface knot can be transformed to an unknotted surface knot or a surface knot which has a diagram with no triple points by a finite number of 1-handle additions. The minimum number of such 1-handles is called the unknotting number or the triple point cancelling number, respectively. In this paper, we give upper bounds and lower bounds of unknotting numbers and triple point cancelling numbers of torus-covering knots, which are surface knots in the form of coverings over the standard torus $T$. Upper bounds are given by using $m$-charts on $T$ presenting torus-covering knots, and lower bounds are given by using quandle colorings and quandle cocycle invariants.Comment: 26 pages, 14 figures, added Corollary 1.7, to appear in J. Knot Theory Ramification

Contributions of 2π2\pi-exchange, 1π1\pi-exchange, and contact three-body forces in NNLO ChEFT to Λ3_\Lambda^3H

Faddeev calculations of hypertriton ($_\Lambda^3$H) separation energy are performed, incorporating all next-to-next-to-leading-order $\Lambda$NN three-body forces (3BFs) in chiral effective field theory: $2\pi$-exchange, $1\pi$-exchange, and contact interactions. The $1\pi$-exchange and contact interactions are rewritten in a form suitable for evaluating partial-wave matrix elements. The $\Lambda$-deuteron folding potentials constructed from these 3BFs are evaluated to demonstrate their contributions to \h3t. The $1\pi$-exchange interaction provides an attractive effect in which the d-state component of the deuteron wave function plays an important role. The attractive contribution tends to cancel the repulsive ones from the $2\pi$-exchange and contact 3BFs. Faddeev calculations show that the net effect of the 3BFs to the \h3t separation energy is small in a range between $-5$ to $+20$ keV, depending on the NN interaction used. Although these results are based on speculative low-energy constants, they can serve as a reference for further investigations.Comment: 6 pages, 4 figure

Faddeev Calculation of Λ3_\Lambda^3H Incorporating 2{\pi} Exchange Λ\LambdaNN Interaction

Faddeev calculations of hypertriton ($_\Lambda^3$H) separation energy are performed, incorporating $2\pi$-exchange $\Lambda$NN three-baryon force. Repulsive contributions of the three-baryon force in the order of 50 $-$ 100 keV are found, depending on the NN interactions employed. The effect is not negligible compared with the small separation-energy of $_\Lambda^3$H and is essential to gauge the two-body $\Lambda$N interactions.Comment: 6 pages, 3 Figure