Algebraic structures on graph cohomology

Details Algebraic structures on graph cohomology Algebraic structures on graph cohomology

2003-07-16

arxiv.org/abs/math/0307218v2

Journal of Knot Theory and Its Ramifications, Vol. 14, No. 5 (2005) 627-640

Mathematics

Geometric Topology

Typos corrected, exposition improved. 14 pages, 2 figures. To appear in J. Knot Theory Ramifications

Scientific paper

10.1142/S0218216505004019

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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