arXiv subjects

Natsuya Takahashi

Publications and source records attributed to Natsuya Takahashi.

6 recordsLinked to original sources

arXiv2026

Trisection genus of knot traces

We classify knot traces with trisection genus at most 2. We give infinitely many torus knots whose traces have trisection genus 3, and infinitely many hyperbolic knots whose traces have trisection genus 4. We also show that there exist infinite families of knots whose traces have arbitrarily large trisection genus. In addition, we determine or give sharp bounds for the trisection genus of the traces of several well-known knots, such as the figure-eight knot, the $(p, pq+1)$-torus knots, and the $(-2, 3, 2n+1)$-pretzel knots.

math.GT↗

arXiv2026

Distinguishing diffeomorphism types of relative trisections

We distinguish diffeomorphism types of relative trisections using a ``capping'' operation, which yields a trisection diagram of a closed 4-manifold from a relative trisection diagram. Using this operation, we give various examples of non-diffeomorphic relative trisections of the same 4-manifold with boundary. We also study how the corresponding trisected 4-manifold changes under the capping operation.

math.GT↗

arXiv2026

Stein fillings of planar contact 3-manifolds with relative trisection genus 2

We study Stein fillings of planar contact 3-manifolds under certain constraints on their relative trisections. We partially classify the diffeomorphism types of such fillings admitting relative trisections with genus at most 2.

math.GT↗

arXiv2025

Exotic 4-manifolds with small trisection genus

We show that there exists an exotic pair of $4$-manifolds with boundary whose trisection genera are $4$. We also construct genus-$3$ relative trisections for an infinite family of contractible $4$-manifolds introduced by Akbulut and Kirby.

math.GT↗

arXiv2024

Non-diffeomorphic minimal genus relative trisections of the same 4-manifold

We show the existence of a $4$-manifold with boundary that admits two non-diffeomorphic minimal genus relative trisections of the same $(g,k;p,b)$-type. To prove this, we introduce a simple operation that produces a trisection diagram of a closed $4$-manifold from a relative trisection diagram.

math.GT↗

arXiv2023

Minimal genus relative trisections of corks

In this paper, we prove that the trisection genus of the Akbulut cork is $3$ and construct infinitely many corks with trisection genus $3$. These results give the first examples of contractible $4$-manifolds whose trisection genera are determined except for the $4$-ball. We also give a lower bound for the trisection genus of a $4$-manifold with boundary. In addition, we construct low genus relative trisection diagrams of an exotic pair of simply-connected $4$-manifolds with $b_2 = 1$.

math.GT↗