Height, trunk and representativity of 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 …
the representativity. First, we give a counterexample for the conjecture which states that the …
[HTML][HTML] Tunnel number degeneration under the connected sum of prime knots
JM Nogueira - Topology and its Applications, 2013 - Elsevier
We study 2-string free tangle decompositions of knots with tunnel number two. As an
application, we construct infinitely many counter-examples to a conjecture in the literature …
application, we construct infinitely many counter-examples to a conjecture in the literature …
Tunnel number of tangles and knots
T Saito - Journal of the Mathematical Society of Japan, 2014 - jstage.jst.go.jp
Tunnel number of tangles and knots Page 1 c©2014 The Mathematical Society of Japan J.
Math. Soc. Japan Vol. 66, No. 4 (2014) pp. 1303–1313 doi: 10.2969/jmsj/06641303 Tunnel …
Math. Soc. Japan Vol. 66, No. 4 (2014) pp. 1303–1313 doi: 10.2969/jmsj/06641303 Tunnel …
Knots and surfaces
M Ozawa - Sugaku Expositions, 2019 - ams.org
AMS :: Sugaku Expositions Skip to Main Content American Mathematical Society American
Mathematical Society MathSciNet Bookstore Publications Publications — Over 100 years of …
Mathematical Society MathSciNet Bookstore Publications Publications — Over 100 years of …
[HTML][HTML] On Heegaard splittings of knot exteriors with tunnel number degenerations
K Morimoto - Topology and its Applications, 2015 - Elsevier
Let K 1, K 2 be two knots with t (K 1)+ t (K 2)> 2 and t (K 1# K 2)= 2. Then, in the present
paper, we will show that any genus three Heegaard splitting of E (K 1# K 2) is strongly …
paper, we will show that any genus three Heegaard splitting of E (K 1# K 2) is strongly …
2-string free tangles and incompressible surfaces
Y Li - Journal of Knot Theory and Its Ramifications, 2009 - World Scientific
2-STRING FREE TANGLES AND INCOMPRESSIBLE SURFACES Page 1 Journal of Knot
Theory and Its Ramifications Vol. 18, No. 8 (2009) 1081–1087 c© World Scientific Publishing …
Theory and Its Ramifications Vol. 18, No. 8 (2009) 1081–1087 c© World Scientific Publishing …
Infinitely many meridional essential surfaces of bounded genus in hyperbolic knot exteriors
JM Nogueira - Geometriae Dedicata, 2021 - Springer
We show the existence of an infinite collection of hyperbolic knots where each of which has
in its exterior meridional essential planar surfaces of arbitrarily large number of boundary …
in its exterior meridional essential planar surfaces of arbitrarily large number of boundary …
On tangle decompositions of tunnel number one links
H Goda, M Ozawa, M Teragaito - Journal of Knot Theory and Its …, 1999 - World Scientific
We will discuss tangle decompositions of tunnel number one links, and show that any tangle
composite tunnel number one link can be obtained as the union of a quasi Hopf tangle and …
composite tunnel number one link can be obtained as the union of a quasi Hopf tangle and …
The number of strings on essential tangle decompositions of a knot can be unbounded
JM Nogueira - Algebraic & Geometric Topology, 2016 - msp.org
An n–string tangle. B; T/is a ball B together with collection of n disjoint arcs T properly
embedded in B, for n 2 N. We say that. B; T/is essential if n is 1 and its arc is knotted, 1 or if n …
embedded in B, for n 2 N. We say that. B; T/is essential if n is 1 and its arc is knotted, 1 or if n …
On composite types of tunnel number two knots
K Morimoto - Journal of Knot Theory and Its Ramifications, 2015 - World Scientific
Let K be a tunnel number two knot. Then, by considering the (g, b)-decompositions, K is one
of (3, 0),(2, 1),(1, 2) or (0, 3)-knots. In this paper, we analyze the connected sum summands …
of (3, 0),(2, 1),(1, 2) or (0, 3)-knots. In this paper, we analyze the connected sum summands …