论文标题
复杂的cartan几何形式的特征形式ii
Characteristic forms of complex Cartan geometries II
论文作者
论文摘要
Dolbeaultsolology中的特征类关系源于圆形cartan几何形状的存在（例如，全体形态的保形结构或全体形态的投射连接）。这些关系可以直接从结构组的表示理论中计算出来，而无需选择任何度量或连接，也可以对歧管的Dolbeault共同体学组进行任何了解。本文通过允许非绘制和非kähler歧管以及在矢量捆绑包的共同体中得出不变的歧管，不仅在标量dolbeault的同一个同居中，以及涉及Chern-simons不变的媒介关系，从而改善了其前身。对于先前在其前身中先前考虑的几何结构，本文给出了更强的结果并简化了计算。它给出了Chern-Simons的第一个结果，即Cartan几何形状的不变。
Characteristic class relations in Dolbeault cohomology follow from the existence of a holomorphic Cartan geometry (for example, a holomorphic conformal structure or a holomorphic projective connection). These relations can be calculated directly from the representation theory of the structure group, without selecting any metric or connection or having any knowledge of the Dolbeault cohomology groups of the manifold. This paper improves on its predecessor by allowing noncompact and non-Kähler manifolds and by deriving invariants in cohomology of vector bundles, not just in scalar Dolbeault cohomology, and computing relations involving Chern--Simons invariants in Dolbeault cohomology. For the geometric structures previously considered in its predecessor, this paper gives stronger results and simplifies the computations. It gives the first results on Chern--Simons invariants of Cartan geometries.
