3 papers
math.SG2025
A vanishing property about the 1-filtered cohomology groups of (4n+2)-dimensional closed symplectic manifolds
Hao Zhuang
This note is a follow-up to our previous work arXiv:2505.14496. For any (4n+2)-dimensional closed symplectic manifold, we find that the dimension of the even-degree part of its 1-f…
math.SG2025
Symplectic semi-characteristics
Hao Zhuang
We study the symplectic semi-characteristic of a closed 4n-dimensional symplectic manifold. First, using the even-degree part of the primitive cohomology, we define the symplectic…
math.DG2024
Kervaire semi-characteristics in KK-theory and an Atiyah type vanishing theorem
Hao Zhuang
On (4n + 1)-dimensional (noncompact) manifolds admitting proper cocompact Lie group actions, we explore the analytic and topological sides of Kervaire semi-characteristics. The ana…