University of Leicester
Browse
VERDIER.pdf (227.57 kB)

Graph homology: Koszul and Verdier duality

Download (227.57 kB)
journal contribution
posted on 2009-07-07, 14:03 authored by Andrey Lazarev, A. A. Voronov
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.

History

Citation

Advances in Mathematics, 2008, 218 (6), pp. 1878-1894.

Published in

Advances in Mathematics

Publisher

Elsevier

issn

0001-8708

Copyright date

2008

Available date

2009-07-07

Publisher version

http://www.sciencedirect.com/science/article/pii/S0001870808000960

Language

en

Usage metrics

    University of Leicester Publications

    Categories

    Keywords

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC