Natsuya Takahashi

activity

20222026

collaborators

6 papers

math.GT2026

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

Nobutaka Asano, Natsuya Takahashi

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 admit…

math.GT2026

Trisection genus of knot traces

Natsuya Takahashi

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…

math.GT2026

Distinguishing diffeomorphism types of relative trisections

Natsuya Takahashi

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 diagr…

math.GT2024

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

Natsuya Takahashi

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…

math.GT2023

Exotic 4-manifolds with small trisection genus

Natsuya Takahashi

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…

math.GT2022

Minimal genus relative trisections of corks

Natsuya Takahashi

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…