Boyu Zhang

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20242026

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5 papers · 1 filter

math.GT2026

The Dax isomorphism for topological $4$ -manifolds

Jianfeng Lin, Yi Xie, Boyu Zhang

Let $X$ be an oriented topological $4$ -manifold with boundary. We establish a Dax isomorphism for the fundamental group of the space of embedded arcs in $X$ . Here, the embedding sp…

math.GT2026

Splitting spheres for $S^{2}$ -links in $S^{4}$

Jianfeng Lin, Yi Xie, Boyu Zhang

We prove that every smooth two-component split sphere link $L ⊔ R \subset S^{4}$ admits infinitely many smooth splitting $3$ -spheres that are topologically non-isotopic. This gene…

math.GT2026

Pseudo-isotopies of 3-manifolds with infinite fundamental groups

Jianfeng Lin, Yi Xie, Boyu Zhang

Suppose $Y$ is a compact, connected, oriented 3-manifold possibly with boundary, such that $π_{1} (Y)$ is infinite. Let $Diff_{\partial} (I \times Y)$ denote the group of s…

math.GT2025

On the mapping class groups of 4-manifolds with 1-handles

Jianfeng Lin, Yi Xie, Boyu Zhang

We develop a framework that generalizes Budney-Gabai's $W_{3}$ invariant on $π_{0} Diff (S^{1} \times D^{3}, \partial)$ to 4-manifolds with 1-handles. As applications, we show that if…

math.GT2025

Dax invariants, light bulbs, and isotopies of symplectic structures

Jianfeng Lin, Weiwei Wu, Yi Xie +1

This paper addresses several isotopy problems on $4$ -manifolds. First, we classify the isotopy classes of embeddings of $Σ$ in $Σ \times S^{2}$ that are geometrically dual to $\{\mbox…

The Dax isomorphism for topological 4-manifolds

Splitting spheres for S2-links in S4

Pseudo-isotopies of 3-manifolds with infinite fundamental groups

On the mapping class groups of 4-manifolds with 1-handles

Dax invariants, light bulbs, and isotopies of symplectic structures

The Dax isomorphism for topological $4$ -manifolds

Splitting spheres for $S^{2}$ -links in $S^{4}$