On the Caldararu and Willwacher conjectures

Alexey Kalugin

On the Caldararu and Willwacher conjectures

Algebraic Geometry 2022-09-13 v2 Algebraic Topology Quantum Algebra

Authors: Alexey Kalugin

Abstract

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 $\mathcal M_{g,n}.$

Keywords

moduli stacks of curves ribbon graph complexes willwacher conjecture caldararu conjecture bridgeland differential string topology

Cite

@article{arxiv.2205.00854,
  title  = {On the Caldararu and Willwacher conjectures},
  author = {Alexey Kalugin},
  journal= {arXiv preprint arXiv:2205.00854},
  year   = {2022}
}

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47 pages

On the Caldararu and Willwacher conjectures

Abstract

Keywords

Cite

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