Download PDFOpen PDF in browserGeneralized Graph Complexes: the Splitting into a Complete GraphEasyChair Preprint 102106 pages•Date: May 18, 2023AbstractGraph complexes are graded vector spaces of formal linear combinations of isomorphism classes of some kind of graphs, with the differential defined by vertex splitting (or, dually, edge contraction). In this paper a generalization, where vertex splitting (i.e. insertion of the complete graph on two vertices) is replaced by insertion of a complete graph, is introduced. Basic properties are shown. Keyphrases: A vertex contraction, An edge contraction, Blow up, Graph complexes, IHXrelation, L_{\infty} algebra, Set Reconstruction Conjecture, Strong homotopy Lie algebra, Witt algebra, complete graphs, generalization, reconstruction conjecture
