Generalized Graph Complexes: the Splitting into a Complete Graph

EasyChair Preprint 10210

Abstract

Graph 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, IHX-relation, L_{\infty} algebra, Set Reconstruction Conjecture, Strong homotopy Lie algebra, Witt algebra, complete graphs, generalization, reconstruction conjecture

@booklet{EasyChair:10210,
  author    = {Valerii Sopin},
  title     = {Generalized Graph Complexes: the Splitting into a Complete Graph},
  howpublished = {EasyChair Preprint 10210},
  year      = {EasyChair, 2023}}