18 citations · 41 across the 9 of their papers we have counts for
9 papers
Signature and crossing number of links
Kai Ishihara, Kei Okada, Koya Shimokawa
This paper investigates the relationship between the signature and the crossing number of knots and links. We refine existing theorems and provide a comprehensive classification of…
Entanglement statistics of polymers in a lattice tube and unknotting of 4-plats
Nicholas R. Beaton, Kai Ishihara, Mahshid Atapour +4
The Knot Entropy Conjecture states that the exponential growth rate of the number of -edge lattice polygons with knot-type is the same as that for unknot polygons. Moreover,…
Handlebody decompositions of 3-manifolds and polycontinuous patterns
Naoki Sakata, Ryosuke Mishina, Masaki Ogawa +4
We introduce the concept of a handlebody decomposition of a 3-manifold, a generalization of a Heegaard splitting, or a trisection. We show that two handlebody decompositions of a c…
Neighborhood equivalence for multibranched surfaces in 3-manifolds
Kai Ishihara, Yuya Koda, Makoto Ozawa +1
A multibranched surface is a 2-dimensional polyhedron without vertices. We introduce moves for multibranched surfaces embedded in a 3-manifold, which connect any two multibranched…
Characterising knotting properties of polymers in nanochannels
Nicholas R. Beaton, Jeremy W. Eng, Kai Ishihara +2
Using a lattice model of polymers in a tube, we define one way to characterise different configurations of a given knot as either "local" or "non-local" and, for several ring polym…
Complete classification of generalized crossing changes between GOF-knots
Kai Ishihara, Matt Rathbun
We analyze all monodromies of genus one fibered knots that possess clean or once-unclean arcs, and use this to determine all manifolds containing genus one fibered knots with gener…
Coherent band pathways between knots and links
Dorothy Buck, Kai Ishihara
We categorise coherent band (aka nullification) pathways between knots and 2-component links. Additionally, we characterise the minimal coherent band pathways (with intermediates)…
Band surgeries and crossing changes between fibered links
Dorothy Buck, Kai Ishihara, Matt Rathbun +1
We characterize cutting arcs on fiber surfaces that produce new fiber surfaces, and the changes in monodromy resulting from such cuts. As a corollary, we characterize band surgerie…
Rational tangle surgery and Xer recombination on catenanes
Isabel K. Darcy, Kai Ishihara, Ram K. Medikonduri +1
The protein recombinase can change the knot type of circular DNA. The action of a recombinase converting one knot into another knot is normally mathematically modeled by band surge…