论文标题
在BV超人群和超级Atiyah班上
On BV Supermanifolds and the Super Atiyah Class
论文作者
论文摘要
我们研究了奇数符号BV超曼菲尔德上的全球和局部形式的几何形状，这些形式是根据基础超曼佛束在1形束的总空间中构建的。我们表明，全球1型是基础超曼佛定义的向量束的扩展。在Holomorphic类别中，我们证明此扩展是在且仅当基本超人的超级Atiyah类消失时才被拆分。这等同于存在霍明型超连接的存在：我们展示了这种条件与复杂超曼佛的特征性非分类几何形状有关。从局部的角度来看，我们证明了变形的de rham双重复合物自然出现是基础超曼佛的de rham/spencer双重复合物的去量化。在Ševera之后，我们表明相关的光谱序列在BV超曼叶夫上产生半敏度，并以超级BV拉普拉斯式的形式差异。
We study global and local geometry of forms on odd symplectic BV supermanifolds, constructed from the total space of the bundle of 1-forms on a base supermanifold. We show that globally 1-forms are an extension of vector bundles defined on the base supermanifold. In the holomorphic category, we prove that this extension is split if and only if the super Atiyah class of the base supermanifold vanishes. This is equivalent to the existence of a holomorphic superconnection: we show how this condition is related to the characteristic non-split geometry of complex supermanifolds. From a local point of view, we prove that the deformed de Rham double complex naturally arises as a de-quantization of the de Rham/Spencer double complex of the base supermanifold. Following Ševera, we show that the associated spectral sequence yields semidensities on the BV supermanifold, together with their differential in the form of a super BV Laplacian.
