Gyo Taek Jin

Polygon Indices and Superbridge Indices of Torus Knots and Links

The minimal number of straight line segments required to form a given knot or link in ℝ3 is determined for a family of torus knots and links.

PRIME KNOTS WITH ARC INDEX UP TO 11 AND AN UPPER BOUND OF ARC INDEX FOR NON-ALTERNATING KNOTS

Every knot can be embedded in the union of finitely many half planes with a common boundary line in such a way that the portion of the knot in each half plane is a properly embedded arc. The minimal number of such half planes is called the arc index of the knot. We have identified all prime knots with arc index up to 11. We also proved that the crossing number is an upperbound of arc index for non-alternating knots. As a result the arc index is determined for prime knots up to twelve crossings.

AN ELEMENTARY SET FOR θn-CURVE PROJECTIONS

A finite set of nontrivial θn-curves is shown to be minimal among those which produce all projections of nontrivial θn-curves.

STRONGLY ALMOST TRIVIAL θ-CURVES

A θ-curve is called almost trivial if it does not contain any non-trivial knot. A θ-curve is called strongly almost trivial if it has a planar projection which does not contain a projection of any non-trivial knot. In this paper, we introduce a method to present strongly almost trivial θ-curves. We also give an almost trivial θ-curve which may not be strongly almost trivial.

P 2 -reducing and toroidal Dehn fillings

Let M be a compact, connected, orientable 3-manifold with a torus boundary component

COEFFICIENTS OF HOMFLY POLYNOMIAL AND KAUFFMAN POLYNOMIAL ARE NOT FINITE TYPE INVARIANTS

\partial_{0}M

ARC INDEX OF PRETZEL KNOTS OF TYPE ( p, q, r)

. A slope on

A COMPUTATION OF SUPERBRIDGE INDEX OF KNOTS

\partial_{0}M

QUADRISECANT APPROXIMATION OF HEXAGONAL TREFOIL KNOT

is the isotopy class of an unoriented essential simple loop. For a slope r , the manifold obtained from M by r-Dehn filling is M ( r ) = M

θ-CURVE POLYNOMIALS AND FINITE-TYPE INVARIANTS

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