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On spaces of connected graphs I: Properties of Ladders
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We examine spaces of connected tri-/univalent graphs subject to local relations which are motivated by the theory of Vassiliev invariants. It is shown that the behaviour of ladder-like subgraphs is strongly related to the parity of the number of rungs: there are similar relations for ladders of even and odd lengths, respectively. Moreover, we prove that - under certain conditions - an even number of rungs may be transferred from one ladder to another.
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M. Kontsevich's graph complexes and universal structures on graded symplectic manifolds
For every d at least 2, the full Kontsevich graph complex maps injectively into the Chevalley-Eilenberg complex of the n=d-1 Schouten algebra, so its zeroth cohomology acts via L-infinity automorphisms on graded sympl...
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