arXiv subjects

Tatsumasa Suzuki

Publications and source records attributed to Tatsumasa Suzuki.

5 recordsLinked to original sources

arXiv2026

On the Ozsváth-Szabó $d$-invariants for almost simple linear graphs

Karakurt and Şavk computed the Ozsváth-Szabó $d$-invariants of Brieskorn homology $3$-spheres arising as surgeries on almost simple linear graphs. In this paper, we refine their formula for these $d$-invariants. Furthermore, we present infinite families of examples for which the inequalities appearing in this refinement are equalities, as well as infinite families for which they are strict. As an application, we derive consequences for the knot concordance group.

math.GT↗

arXiv2025

The pretzel knot $P(4, -3, 5)$ is not squeezed

We prove that an infinite family of three-strand pretzel knots is not squeezed. In particular, we show that $P(4, -3, 5)$ is not squeezed. This answers a question posed by Lewark (2024). Our proof is obtained by comparing the Rasmussen invariant with the $q_M$-invariant introduced by Iida and Taniguchi.

math.GT↗

arXiv2025

The non-simply connected Price twist for the 4-sphere

A cutting and pasting operation on a $P^2$-knot $S$ in a $4$-manifold is called the Price twist. The Price twist for the $4$-sphere $S^4$ yields at most three $4$-manifolds up to diffeomorphism, namely, the $4$-sphere $S^4$, the other homotopy $4$-sphere $Σ_{S}(S^4)$ and a non-simply connected $4$-manifold $τ_{S}(S^4)$. In this paper, we study some properties and diffeomorphism types of $τ_{S}(S^4)$ for $P^2$-knots $S$ of Kinoshita type.

math.GT↗

arXiv2023

Constructions of homotopy 4-spheres by pochette surgery

The pochette surgery, which was discovered by Iwase and Matsumoto, is a generalization of the Gluck surgery. In this paper we construct infinitely many embeddings of a pochette into the 4-sphere and prove that homotopy 4-spheres obtained from surgeries along these embedded pochettes are all diffeomorphic to the 4-sphere.

math.GT↗

arXiv2022

Pochette surgery of 4-sphere

Iwase and Matsumoto defined `pochette surgery' as a cut-and-paste on 4-manifolds along a 4-manifold homotopy equivalent to $S^2\vee S^1$. The first author in [10] studied infinitely many homotopy 4-spheres obtained by pochette surgery. In this paper we compute the homology of pochette surgery of any homology 4-sphere by using `linking number' of a pochette embedding. We prove that pochette surgery with the trivial cord does not change the diffeomorphism type or gives a Gluck surgery. We also show that there exist pochette surgeries on the 4-sphere with a non-trivial core sphere and a non-trivial cord such that the surgeries give the 4-sphere.

math.GT↗