A detailed look on actions on Hochschild complexes especially the degree 1 coproduct and actions on loop spaces

نویسندگان

چکیده

We explain our previous results about Hochschild actions (2007/2008) pertaining, in particular, to the coproduct, which appeared a different form work by Goresky and Hingston (2009), provide fresh look at results. recall general action, specialize aforementioned coproduct prove that assumption of commutativity, made for convenience article (2008), is not needed. give detailed background material on loop spaces, complexes dualizations, discuss details extensions these techniques all operations given two articles (2007/2008). With respect we show well defined modulo constant loops going one step further case graded Gorenstein Frobenius algebra, reduced normalized complex. several other aspects such as “time reversal” duality homotopies induced it. This provides cohomology operation homotopy anti-symmetrization coproduct. The obstruction again vanishes complex if algebra Gorenstein. Further structures “animation”, BV structure, coloring chains cochains, Gerstenhaber double bracket are briefly treated.

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ژورنال

عنوان ژورنال: Journal of Noncommutative Geometry

سال: 2022

ISSN: ['1661-6960', '1661-6952']

DOI: https://doi.org/10.4171/jncg/470