On the intersection forms of spin 4-manifolds bounded by spherical 3-manifolds

关于自交角有下界的测地线的豪斯多夫维数

On the Hausdorff dimension of geodesics with bounded self-intersection angle

本文推广 Birman 和 Series 的结果，证明自交角有下界的测地线集合以及不围成测地三角形的测地线集合的豪斯多夫维数均为零。

Constraints on intersection forms of spin 4-manifolds bounded by Seifert rational homology 3-spheres in terms of $\barμ$ and $κ$ invariants

We give some constraints on intersection forms of spin 4-manifolds bounded by Seifert rational homology 3-spheres in terms of the $\barμ$ invariant and compare them with those in terms of the $κ$ invariant. We also show that the difference between $κ$ and $-\barμ$ for a Seifert rational homology 3-sphere is at most 2, and under certain extra conditions the difference is 0.

Intersection properties of stable subgroups and bounded cohomology

We show that a finite collection of stable subgroups of a finitely generated group has finite height, finite width and bounded packing. We then use knowledge about intersections of conjugates to characterize finite families of quasimorphisms on hyperbolically embedded subgroups that can be to simultaneously extended to the ambient group.

On intersection forms of definite 4-manifolds bounded by a rational homology 3-sphere

We show that, if a rational homology 3-sphere $Y$ bounds a positive definite smooth 4-manifold, then there are finitely many negative definite lattices, up to the stable-equivalence, which can be realized as the intersection form of a smooth 4-manifold bounded by $Y$. To this end, we make use of constraints on definite forms bounded by $Y$ induced from Donaldson's diagonalization theorem, and correction term invariants due to Frøyshov, and Ozsváth and Szabó. In particular, we prove that all spherical 3-manifolds satisfy such finiteness property.

球面扭转、关系和K3表面导出范畴自同构群的中心

Spherical twists, relations and the center of autoequivalence groups of K3 surfaces

本文研究K3表面导出范畴自同构群的中心，通过球面扭转的交数性质，探讨其与映射类群的类比关系，并分类由两个球面扭转生成的子群。

有界 $\u001dmathfrak{sp}_4$-层状结构及其相交坐标

Bounded $\mathfrak{sp}_4$-laminations and their intersection coordinates

本文在标记曲面上构造有理有界 $\u001dmathfrak{sp}_4$-层状结构，用 $\u001dmathfrak{sp}_4$-网、有理测度与相交坐标刻画 Fock–Goncharov 有理热带点，并证明坐标双射。