Homology, Homotopy and Applications

Volume 11 (2009)

Number 2

A simplicial $A_{\infty}$-operad acting on $R$-resolutions

Pages: 55 – 73

DOI: http://dx.doi.org/10.4310/HHA.2009.v11.n2.a5


Tilman Bauer (Faculteit der exacte wetenschappen, Vrije Universiteit Amsterdam, The Netherlands)

Assaf Libman (Department of Mathematical Sciences, King’s College, University of Aberdeen, Scotland, United Kingdom)


We construct a combinatorial model of an $A_{\infty}$-operad which acts simplicially on the cobar resolution (not just its total space) of a simplicial set with respect to a ring $R$.


$A_{\infty}$-monad; completion; cobar resolution

2010 Mathematics Subject Classification

18C15, 18D50, 55P60

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