论文标题
在Caldararu和Willwacher猜想上
On the Caldararu and Willwacher conjectures
论文作者
论文摘要
在本文中，我们研究了光滑曲线的模量堆栈的共同点$ \ MATHCAL M_ {G，N} $与功能界图复合物的共同体学之间的关系。这项工作的主要结果是T. Willwacher的猜想和A. C $ \ Check {\ Mathrm a} $ LD $ \ check {\ Mathrm a} $ raru关于Bridgeland差异的共同体学的猜想。我们还讨论了与字符串拓扑结构和Chan-Galatius-Payne定理有关的关系，内容涉及$ \ Mathcal M_ {G，N}的紧凑型共同体的重量零部分。
In the present paper, we study a relation between the cohomology of moduli stacks of smooth and proper curves $\mathcal M_{g,n}$ and the cohomology of ribbon graph complexes. The main results of this work are proofs of T. Willwacher's conjecture and A. C$\check{\mathrm a}$ld$\check{\mathrm a}$raru's conjecture about the cohomology of the Bridgeland differential. We also discuss the relation to string topology and the Chan-Galatius-Payne theorem about the weight zero part of the compactly supported cohomology of $\mathcal M_{g,n}.$
