We consider links that are alternating on surfaces embedded in a compact 3-manifold. We
show that under mild restrictions, the complement of the link decomposes into simpler …

" Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics.
This enyclopedia is filled with valuable information on a rich and fascinating subject."–Ed …

In this thesis we study several classes of knots and links which have alternating projections
onto closed orientable surfaces. We are particularly interested in surface-alternating …

We study near-alternating links whose diagrams satisfy conditions generalized from the
notion of semi-adequate links. We extend many of the results known for adequate knots …

In this paper, we investigate three geometrical invariants of knots, the height, the trunk and
the representativity. First, we give a counterexample for the conjecture which states that the …

This note gives the first example of a hyperbolic knot in the 3-sphere that lacks a
nonorientable essential spanning surface; this disproves the Strong Neuwirth Conjecture …

AMS :: Sugaku Expositions Skip to Main Content American Mathematical Society American
Mathematical Society MathSciNet Bookstore Publications Publications — Over 100 years of …

Given a diagram D⊂ S2 of a knot K⊂ S3, one can construct two spanning surfaces B and W
for K by shading each of the disks of S2\D one of two colors (say, dark or light) such that …

Let K be a nontrivial knot in 𝕊 3. It was conjectured that there exists a Neuwirth surface for K.
That is, a closed surface in 𝕊 3 containing the knot K as a nonseparating curve and such that …

It is a well-known procedure for constructing a torus knot or link that first we prepare an
unknotted torus and meridian disks in its complementary solid tori, and second we smooth …