Oriented Getzler-Kapranov complexes and framed curves

TL;DR

This paper introduces oriented Getzler-Kapranov complexes, generalizing Merkulov's oriented graph complex, and explores their connections to moduli space cohomology, ribbon graphs, and string topology motivic structures.

Contribution

It presents the construction and study of oriented Getzler-Kapranov complexes and analyzes their relations to various geometric and topological structures.

Findings

Established links between oriented Getzler-Kapranov complexes and moduli space cohomology

Connected these complexes to ribbon graph complexes and motivic structures in string topology

Extended the framework of graph complexes to oriented and framed curve contexts

Abstract

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.