arXiv subjects
Publications and source records attributed to Alexey Kalugin.
In this note, we study A. Beilinson's gluing for perverse sheaves in the case of the diagonal arrangement and its relation to the Grothendieck-Teichmüller group. We also explain a relation to the Etingof-Kazhdan quantisation
In the present paper, we introduce and study oriented Getzler-Kapranov complexes. These complexes are generalizations of S. Merkulov's oriented graph complex. We investigate their relation to the cohomology of moduli spaces of complex and tropical curves, ribbon graph complexes, and motivic structures in string topology.
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 $\mathcal M_{g,n}.$
In this paper, we study the so-called Getzler-Kapranov complexes and their relation to the cohomology of moduli stacks of curves.
In a present note we give a new proof of Etingof-Kazhdan quantization theorem.
In present paper we develop categorical formalism of Verdier duality for diagrams of topoi. We use this approach to construct Grothendieck six operations formalism.