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Bar constructions and
Quillen homology of modules over operads
John E Harper |
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Algebraic & Geometric Topology 10 (2010) 87–136
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Abstract |
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We show that topological Quillen homology of algebras and modules over operads in symmetric spectra can be calculated by realizations of simplicial bar constructions. Working with several model category structures, we give a homotopical proof after showing that certain homotopy colimits in algebras and modules over operads can be easily understood. A key result here, which lies at the heart of this paper, is showing that the forgetful functor commutes with certain homotopy colimits. We also prove analogous results for algebras and modules over operads in unbounded chain complexes. |
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Keywords
symmetric spectra, model category, operads, Quillen
homology, chain complex
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Mathematical Subject Classification 2000
Primary: 55P43, 55P48, 55U35, 18G55
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References |
Publication
Received: 14 February 2008
Revised: 27 September 2009
Accepted: 7 October 2009
Published: 10 January 2010
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Authors |
| John E Harper | |
| Institut de Géométrie, Algèbre et
Topologie EPFL CH-1015 Lausanne Switzerland |
Department of Mathematics University of Notre Dame Notre Dame, IN 46556 USA |
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