Algebraic structures on graph cohomology
Geometric Topology
2007-05-23 v2
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.
Cite
@article{arxiv.math/0307218,
title = {Algebraic structures on graph cohomology},
author = {Alberto S. Cattaneo and Paolo Cotta-Ramusino and Riccardo Longoni},
journal= {arXiv preprint arXiv:math/0307218},
year = {2007}
}
Comments
Typos corrected, exposition improved. 14 pages, 2 figures. To appear in J. Knot Theory Ramifications