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ALGEBRAIC STRUCTURES ON GRAPH COHOMOLOGY
Abstract
We define algebraic structures on graph cohomology and prove that they correspond to algebraic structures on the cohomology of the spaces of imbeddings of S1 or ℝ into ℝn. As a corollary, we deduce the existence of an infinite number of nontrivial cohomology classes in Imb(S1, ℝn) when n is even and greater than 3. Finally, we give a new interpretation of the anomaly term for the Vassiliev invariants in ℝ3.
AMSC: Primary 58D10, Secondary 81Q30
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