5 papers · 1 filter
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…
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…
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…
Analytic and topological realizations of the invariant Thom-Smale complex
Hao Zhuang
With the smooth action of a connected compact Lie group G, we realize the G-invariant Thom-Smale complex in an analytic way using the G-invariant Witten instanton complex. Both com…