On a cohomology of digraphs and Hochschild cohomol

Authors: Alexander Grigor’yan Yuri Muranov ShingTung Yau

Publish Date: 2015/03/20

Volume: 11, Issue: 2, Pages: 209-230

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Abstract

We use a differential form cohomology theory on transitive digraphs to give a new proof of a theorem of Gerstenhaber and Schack about isomorphism between simplicial cohomology and Hochschild cohomology of a certain algebra associated with the simplicial complexA Grigor’yan was partially supported by SFB 701 of German Research Council and by Visiting Grants of Harvard University and MSC Tsinghua University Yu Muranov was partially supported by SFB 701 of German Research Council and by Visiting Grants of Harvard University ST Yau was partially supported by the Grant “Geometry and Topology of Complex Networks” no FA95501310097The first author is grateful to Xueping Huang for bringing to his attention the paper 4 The authors are grateful to an unnamed referee for useful remarks and suggestions leading to improvement of the paper This work was done during the visit of the second author to the University of Bielefeld and the visits of the first and second authors to the Harvard University The financial support and hospitality of the both institutions are gratefully acknowledged

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