3,193 research outputs found
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 . Upper bounds are
given by using -charts on 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 -exchange, -exchange, and contact three-body forces in NNLO ChEFT to H
Faddeev calculations of hypertriton (H) separation energy are
performed, incorporating all next-to-next-to-leading-order NN
three-body forces (3BFs) in chiral effective field theory: -exchange,
-exchange, and contact interactions. The -exchange and contact
interactions are rewritten in a form suitable for evaluating partial-wave
matrix elements. The -deuteron folding potentials constructed from
these 3BFs are evaluated to demonstrate their contributions to \h3t. The
-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 -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 to 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 H Incorporating 2{\pi} Exchange NN Interaction
Faddeev calculations of hypertriton (H) separation energy are
performed, incorporating -exchange 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 H and is
essential to gauge the two-body N interactions.Comment: 6 pages, 3 Figure
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