Algebraic structures on graph cohomology

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

Algebraic structures on graph cohomology

Authors

Cattaneo, Alberto S.

Cotta-Ramusino, Paolo

Longoni, Riccardo

Description

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