Makoto Ozawa

collaborators

13 papers

math.GT2026

Essential-Surface Complexes of Knot Exteriors: Image, Kernel, and Reconstruction

Makoto Ozawa

This is an expository article. The curve complex of a surface is deliberately forgetful, yet in most cases its automorphism group recovers the mapping class group. We explain what…

math.GT2026

Ropelength-Filtered Essential Surface Spaces

Makoto Ozawa

We develop a filtered geometric framework for essential surfaces in knot exteriors. Let $γ$ be a unit-thickness representative of a knot type $K$ with $Len (γ) \leq Λ$ , and le…

math.GT2026

Density and Compression on Lattice-Knot Merge Trees

Makoto Ozawa

Ropelength is usually studied as a minimization problem for one knot at a time. We instead use ropelength to filter the space of all realizations of a knot type. For a knot type $K…

math.GT2026

Merge Trees of Length-Filtered Lattice Knot Spaces

Makoto Ozawa

We study length-filtered BFACF graphs of self-avoiding polygons in the simple cubic lattice, with merge heights recording the least length cap needed to connect configurations. We…

math.GT2026

Ropelength-Filtered Swept-Area Geometry

Makoto Ozawa

This paper studies the swept-area cost of isotopies between thick knot representatives when the isotopy is required to stay inside a ropelength window: every intermediate curve has…

math.GT2026

Ropelength-Filtered Reidemeister Graphs

Makoto Ozawa

We prove relative smoothing with uniform reach control for one-parameter families of positive-reach $C^{1, 1}$ knots and combine it with relative multijet transversality to obtain p…

math.GT2026

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 $D$ be a Euclidean-invariant, scale-covariant size…

math.GT2026

Ropelength-Filtered Knot Densities

Makoto Ozawa

We study scale-invariant $p$ -densities of knot types in Euclidean three-space, defined as the infimum over representatives of the length divided by an $L^{p}$ -type mean of the pairwi…

math.GT2026

Ropelength-Filtered Knot Spaces

Makoto Ozawa

Ropelength is usually studied as a minimisation problem for one knot at a time. Here we instead use ropelength to filter the space of all realisations of a knot type. For a knot ty…

math.GT2026

Amicable Knots on Minimal Genus Seifert Surfaces

Makoto Ozawa

For a knot $K \subset S^{3}$ , let $S (K)$ denote the set of non-trivial knot types represented by simple closed curves on a minimal genus Seifert surface of $K$ . We study the relation…

math.GT2026

The realization problem of essential surfaces in knot exteriors

Makoto Ozawa, Jesús Rodríguez-Viorato

We study compact orientable essential surfaces in knot exteriors in the 3-sphere. The genus $g$ , the number of boundary components $b$ , and the boundary slope $p / q$ are fundamental…

math.GT2026

Crossing Numbers of Knots on Closed Surfaces

Makoto Ozawa

Let c(K;F) denote the surface crossing number of a knot K with respect to a closed connected surface F in S^3. We relate c(K;F) to the tunnel number t(K) and to the Heegaard defici…

math.GT2024

A Kuratowski-Type Classification of Critical Complexes for the 3-Sphere

Mario Eudave-Muñoz, Makoto Ozawa

We give a Kuratowski-type classification of a graph-defined class of minimal piecewise-linear obstructions to embeddability in the 3-sphere. A finite simplicial complex $X$ is ca…