On the Caldararu and Willwacher conjectures
Abstract
In the present paper, we study a relation between the cohomology of moduli stacks of smooth and proper curves Mg,n and the cohomology of ribbon graph complexes. The main results of this work are proofs of T. Willwacher's conjecture and A. C ald araru'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 Mg,n.
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