Bar constructions and Quillen homology of modules over operads

Harper, John E¹

¹Institut de Géométrie, Algèbre et Topologie, EPFL, CH-1015 Lausanne, Switzerland, Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA

Algebraic and Geometric Topology, Tome 10 (2010) no. 1, pp. 87-136

Résumé

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.

Détail

DOI : 10.2140/agt.2010.10.87

Keywords: symmetric spectra, model category, operads, Quillen homology, chain complex

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