Cattaneo, A S; Cotta-Ramusino, P; Longoni, R (2005). Algebraic structures on graph cohomology. Journal of Knot Theory and Its Ramifications, 14(5):627-640.
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.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Algebra and Number Theory |
| Uncontrolled Keywords: | Graph cohomology, Vassiliev invariants, configuration spaces, Hopf algebras |
| Language: | English |
| Date: | 2005 |
| Deposited On: | 27 Jan 2010 12:40 |
| Last Modified: | 26 Jun 2022 22:27 |
| Publisher: | World Scientific Publishing |
| ISSN: | 0218-2165 |
| Additional Information: | Electronic version of an article published as [J. Knot Theory Ramifications 14 (2005), no. 5, 627--640] © 2005 copyright World Scientific Publishing Company [http://www.worldscinet.com/jktr/jktr.shtml] |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.1142/S0218216505004019 |
Cattaneo, A S