Graph Complexes and higher genus Grothendieck-Teichmüller Lie algebras

2021/05/05 by Felder, Matteo · 1 citation
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2105.02056

Abstract

We give a presentation in terms of generators and relations of the cohomology in degree zero of the Campos-Willwacher graph complexes associated to compact orientable surfaces of genus g. The results carry a natural Lie algebra structure, and for g=1 we recover Enriquez' elliptic Grothendieck-Teichmüller Lie algebra. In analogy to Willwacher's theorem relating Kontsevich's graph complex to Drinfeld's Grothendieck-Teichmüller Lie algebra, we call the results higher genus Grothendieck-Teichmüller Lie algebras. Moreover, we find that the graph cohomology vanishes in negative degrees.

Cited by

• Drinfeld associators and Kashiwara-Vergne associators in higher genera

Related

• Stable cohomology of graph complexes
• Filtrations on graph complexes and the Grothendieck-Teichm "uller Lie\n algebra in depth two
• Notes on Algebraic Operads, Graph Complexes, and Willwacher's Construction
• Deformation theory of the wheeled properad of strongly homotopy Lie bialgebras and graph complexes
• Weight 11 Compactly Supported Cohomology of Moduli Spaces of Curves in excess four