8 papers
Instanton construction of the mapping cone Thom-Smale complex
Hao Zhuang
The wedge by a smooth closed -form induces the mapping cone de Rham cochain complex. This complex is quasi-isomorphic to the mapping cone Thom-Smale cochain complex. In this…
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…
A Serre type vanishing property of the twisted primitive cohomology
Hao Zhuang
We prove a Serre type vanishing property for the twisted primitive cohomology of a symplectic manifold. It is based on Tseng and Zhou's vanishing property under the symplectic flat…
Mapping cone Thom forms
Hao Zhuang
For the de Rham mapping cone cochain complex induced by a smooth closed 2-form, we explicitly write down the associated mapping cone Thom form in the sense of Mathai-Quillen. Our c…
Transgression in the primitive cohomology
Hao Zhuang
We study the Chern-Weil theory for the primitive cohomology of a symplectic manifold. First, given a symplectic manifold, we review the superbundle-valued forms on this manifold an…
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…