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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.
| 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: | 07 Jan 2025 04:38 |
| 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