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Graph homology:Koszul and Verdier duality

Lazarev, Andrey and Voronov, Alexander (2008) Graph homology:Koszul and Verdier duality. Advances in Mathematics, 218 (6). pp. 1878-1894. ISSN 0001-8708

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Abstract

We show that Verdier duality for certain sheaves on the moduli spaces of graphs associated to differential graded operads corresponds to the cobar-duality of operads (which specializes to Koszul duality for Koszul operads). This in particular gives a conceptual explanation of the appearance of graph cohomology of both the commutative and Lie types in computations of the cohomology of the outer automorphism group of a free group. Another consequence is an explicit computation of dualizing sheaves on spaces of metric graphs, thus characterizing to which extent these spaces are different from oriented orbifolds. We also provide a relation between the cohomology of the space of metric ribbon graphs, known to be homotopy equivalent to the moduli space of Riemann surfaces, and the cohomology of a certain sheaf on the space of usual metric graphs.

Item Type: Article
Journal or Publication Title: Advances in Mathematics
Uncontrolled Keywords: Graph homology ; Cyclic operad ; Koszul duality ; Constructible sheaf ; Verdier duality ; Simplicial complex
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 59740
Deposited By: ep_importer_pure
Deposited On: 04 Nov 2012 16:08
Refereed?: Yes
Published?: Published
Last Modified: 01 Apr 2014 11:46
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/59740

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