On interrelations between graph complexes
Abstract
We study Maxim Kontsevich's graph complex GCd for any integer d as well as its oriented and targeted versions, and show new short proofs of the theorems due to Thomas Willwacher and Marko Zivkovic which establish isomorphisms of their cohomology groups. A new result relating the cohomology of the sourced-targeted graph complex in dimension d+1 with the direct sum of two copies of the cohomology group of Maxim Kontsevich's graph complex GCd in dimension d is obtained. We introduce a new graph complex spanned by purely trivalent graphs and show that its cohomology is isomorphic to H(GCd).
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