W. Niu

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8 papers · 1 filter

math.GT2026

Mapping class groups of negatively curved four-manifolds

Weizhe Niu

For every closed oriented smooth four-manifold $M$ admitting a metric of strictly negative sectional curvature, we prove that $\dim_{\mathbb{Q}}H_1(T(M);\mathbb{Q})=\dim_{\mathbb{Q…

math.GT2026

A survey on mapping class groups of 3-manifolds

Philipp Bader, Rachael Boyd, Giulia Carfora +8

We survey computations and tools concerning the mapping class group of a compact, oriented, connected 3-manifold $M$ . We provide a guide to the literature and sketch proofs for var…

math.GT2026

Embedded surfaces with trivial extendable mapping class groups in simply connected $4$ -manifolds

Weizhe Niu

For every $g \geq 3$ , every closed, connected, oriented, simply connected smooth $4$ -manifold $X$ , and every knot $K \subset S^{3}$ , we construct infinitely many pairwise topologically…

math.GT2026

Image nonconcordance of positive-genus $π_{1}$ -injective surfaces

Weizhe Niu

We construct, for every $g \geq 2$ , infinite families of homotopic smooth embeddings of a closed genus- $g$ surface whose images are pairwise not smoothly image-concordant, while eac…

math.GT2026

Triple torsion, triple cup products, and embedding obstructions for rational homology 3-spheres

Weizhe Niu

Freedman and Krushkal introduced a triple torsion linking form for rational homology $3$ -spheres and used it to obstruct locally flat embeddings in $S^{4}$ . For every odd prime $p$ ,…

math.GT2026

Extendable mapping classes of knotted surfaces obtained by rim surgery in $S^{4}$

Weizhe Niu

Let $Σ_{g}^{0} \subset S^{4}$ , $g \geq 3$ , be the standard unknotted closed oriented surface, and let $a \subset Σ_{g}^{0}$ be an oriented nonseparating curve. For every nontrivial knot $J\subset…

math.GT2026

Brunnian spanning 3-disks for the 2-unlink in the 4-sphere

Weizhe Niu

We show that the $2$ -component unlink in $S^{4}$ admits infinitely many isotopy classes of spanning $3$ -disks that are Brunnian.

math.GT2025

On the mapping class group of 4-dimensional 1-handlebodies via Budney-Gabai invariants

Weizhe Niu

We define an invariant $(W_{3})_{m}$ for $π_{0} Diff (♮_{m} S^{1} \times D^{3}, \partial)$ for $m \geq 1$ that generalizes Budney--Gabai's $W_{3}$ invariant. We give a computational f…

Mapping class groups of negatively curved four-manifolds

A survey on mapping class groups of 3-manifolds

Embedded surfaces with trivial extendable mapping class groups in simply connected 4-manifolds

Image nonconcordance of positive-genus π1​-injective surfaces

Triple torsion, triple cup products, and embedding obstructions for rational homology 3-spheres

Extendable mapping classes of knotted surfaces obtained by rim surgery in S4

Brunnian spanning 3-disks for the 2-unlink in the 4-sphere

On the mapping class group of 4-dimensional 1-handlebodies via Budney-Gabai invariants

Embedded surfaces with trivial extendable mapping class groups in simply connected $4$ -manifolds

Image nonconcordance of positive-genus $π_{1}$ -injective surfaces

Extendable mapping classes of knotted surfaces obtained by rim surgery in $S^{4}$