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Hypercommutative Algebras and Cyclic Cohomology
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 1
2017 (English)In: The Michigan mathematical journal, ISSN 0026-2285, E-ISSN 1945-2365, Vol. 66, no 3, 533-547 p.Article in journal (Refereed) Published
Abstract [en]

We introduce a chain model for the Deligne-Mumford operad formed by homotopically trivializing the circle in a chain model for the framed little disks. We then show that under degeneration of the Hochschild to cyclic cohomology spectral sequence, a known action of the framed little disks on Hochschild cochains lifts to an action of this new chain model. We thus establish homotopy hypercommutative algebra structures on both Hochschild and cyclic cochain complexes, and we interpret the gravity brackets on cyclic cohomology as obstructions to degeneration of this spectral sequence. Our results are given in the language of deformation complexes of cyclic operads.

Place, publisher, year, edition, pages
2017. Vol. 66, no 3, 533-547 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-149041DOI: 10.1307/mmj/1496822426ISI: 000412791200005OAI: oai:DiVA.org:su-149041DiVA: diva2:1157491
Available from: 2017-11-16 Created: 2017-11-16 Last updated: 2017-11-16Bibliographically approved

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