Abstract. A pseudodiagram is a diagram of a knot with some crossing infor-mation missing. We review and expand the theory of pseudodiagrams intro-duced by R. Hanaki. We then extend this theory to the realm of virtual knots, a generalization of knots. In particular, we analyze the trivializing number of a pseudodiagram, i.e. the minimum number of crossings that must be resolved to produce the unknot. We consider how much crossing information is needed in a virtual pseudodiagram to identify a non-trivial knot, a classical knot, or a non-classical knot. We then apply pseudodiagram theory to develop new upper bounds on unknotting number, virtual unknotting number, and genus. 1
Abstract Kuperberg [15] has shown that a virtual knot diagram corre-sponds (up to generalized Reidem...
We prove for rational knots a conjecture of Adams et al. that an alternating unknotting number one k...
We prove for rational knots a conjecture of Adams et al. that an alternating unknotting number one k...
Classical knots in R3 can be represented by diagrams in the plane. These diagrams are formed by curv...
The aim of the present paper is to prove that the minimal number of virtual crossings for some famil...
The aim of the present paper is to prove that the minimal number of virtual crossings for some famil...
Unknotting moves, local deformations that can change any knot into the unknot, have long been a subj...
AbstractKishino's knot is not detected by the fundamental group or the bracket polynomial. However, ...
Unknotting moves, local deformations that can change any knot into the unknot, have long been a subj...
Unknotting moves, local deformations that can change any knot into the unknot, have long been a subj...
AbstractBy using a result of L. Rudolph concerning the four-genus of a classical knot, we calculate ...
AbstractKishino's knot is not detected by the fundamental group or the bracket polynomial. However, ...
Abstract Kuperberg [15] has shown that a virtual knot diagram corre-sponds (up to generalized Reidem...
Abstract Kuperberg [15] has shown that a virtual knot diagram corre-sponds (up to generalized Reidem...
Abstract Kuperberg [15] has shown that a virtual knot diagram corre-sponds (up to generalized Reidem...
Abstract Kuperberg [15] has shown that a virtual knot diagram corre-sponds (up to generalized Reidem...
We prove for rational knots a conjecture of Adams et al. that an alternating unknotting number one k...
We prove for rational knots a conjecture of Adams et al. that an alternating unknotting number one k...
Classical knots in R3 can be represented by diagrams in the plane. These diagrams are formed by curv...
The aim of the present paper is to prove that the minimal number of virtual crossings for some famil...
The aim of the present paper is to prove that the minimal number of virtual crossings for some famil...
Unknotting moves, local deformations that can change any knot into the unknot, have long been a subj...
AbstractKishino's knot is not detected by the fundamental group or the bracket polynomial. However, ...
Unknotting moves, local deformations that can change any knot into the unknot, have long been a subj...
Unknotting moves, local deformations that can change any knot into the unknot, have long been a subj...
AbstractBy using a result of L. Rudolph concerning the four-genus of a classical knot, we calculate ...
AbstractKishino's knot is not detected by the fundamental group or the bracket polynomial. However, ...
Abstract Kuperberg [15] has shown that a virtual knot diagram corre-sponds (up to generalized Reidem...
Abstract Kuperberg [15] has shown that a virtual knot diagram corre-sponds (up to generalized Reidem...
Abstract Kuperberg [15] has shown that a virtual knot diagram corre-sponds (up to generalized Reidem...
Abstract Kuperberg [15] has shown that a virtual knot diagram corre-sponds (up to generalized Reidem...
We prove for rational knots a conjecture of Adams et al. that an alternating unknotting number one k...
We prove for rational knots a conjecture of Adams et al. that an alternating unknotting number one k...