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.
Algebraic structures on graph cohomology / A. Cattaneo, P. Cotta-Ramusino, R. Longoni. - In: JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS. - ISSN 0218-2165. - 14:5(2005), pp. 627-640. [10.1142/S0218216505004019]
Algebraic structures on graph cohomology
P. Cotta-Ramusino;
2005
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.
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