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Algebraic structures on graph cohomology


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.

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 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.

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 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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Graph cohomology; Vassiliev invariants; configuration spaces; Hopf algebras
Language:English
Date:2005
Deposited On:27 Jan 2010 12:40
Last Modified:06 Dec 2017 20:46
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]
Publisher DOI:https://doi.org/10.1142/S0218216505004019

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