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    Operadic twisting - With an application to Deligne's conjecture

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    Genre
    Journal Article
    Date
    2015-01-01
    Author
    Dolgushev, V
    Willwacher, T
    Subject
    math.RA
    math.RA
    math.KT
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/5834
    
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    DOI
    10.1016/j.jpaa.2014.06.010
    Abstract
    © 2014 Elsevier B.V. We study categorial properties of the operadic twisting functor Tw. In particular, we show that Tw is a comonad. Coalgebras of this comonad are operads for which a natural notion of twisting by Maurer-Cartan elements exists. We give a large class of examples, including the classical cases of the Lie, associative and Gerstenhaber operads, and their infinity-counterparts Lie∞, As∞, Ger∞. We also show that Tw is well behaved with respect to the homotopy theory of operads. As an application we show that every solution of Deligne's conjecture is homotopic to a solution that is compatible with twisting.
    Citation to related work
    Elsevier BV
    Has part
    Journal of Pure and Applied Algebra
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    For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/5816
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