Algebraic structures on graph cohomology

Alberto S. Cattaneo; Paolo Cotta-Ramusino; Riccardo Longoni

doi:10.1142/s0218216505004019

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Algebraic structures on graph cohomology

Alberto S. Cattaneo·Paolo Cotta-Ramusino·Riccardo Longoni

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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 S^1 or R into R^n. As a corollary, we deduce the existence of an infinite number of nontrivial cohomology classes in Imb(S^1,R^n) when n is even and greater than 3. Finally, we give a new interpretation of the anomaly term for the Vassiliev invariants in R^3.

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Alberto S. Cattaneo, Paolo Cotta-Ramusino, Riccardo Longoni. 2005-03-18. Algebraic structures on graph cohomology. https://doi.org/10.1142/s0218216505004019

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