13 papers
An Image--Kernel--Reconstruction Program for Essential-Surface Complexes of Knot Exteriors
Makoto Ozawa
We study the action of the meridian-preserving mapping class group of a knot exterior E on the disjointness complex of connected two-sided orientable essential surfaces, with natur…
A Geometric Finiteness Theory for Essential Surfaces in Knot Exteriors
Makoto Ozawa
We develop a relative geometric finiteness theory for essential surfaces in knot exteriors. Let be a unit-thickness representative of a knot type , with $\operatorname{Len}…
Discrete p-Density and Compression Radii of Lattice Knots
Makoto Ozawa
We introduce a finite-state framework for discrete -density and compression-radius profiles of lattice knots. At a lattice length level , we consider representatives of a fix…
Finite Knot Theory via Ropelength-Filtered Reidemeister Graphs
Makoto Ozawa
We develop a finite-recognition framework for knot types using ropelength-filtered Reidemeister graphs. For a fixed projection direction, bounded-ropelength thick-knot spaces deter…
Geometric densities and compression radii of knot types
Makoto Ozawa
We introduce scale-free compression radii and packing ratios of knot types and clarify their relation to geometric densities. Let be a Euclidean-invariant, scale-covariant size…
Discrete Knot Theory via Lattice-Filtered Move Graphs
Makoto Ozawa
We introduce lattice-filtered move graphs as finite-state experimental models for knot types. At level , vertices are lattice-polygon representatives of a fixed knot type with l…