Bar constructions and Quillen homology of modules over operads

Details Bar constructions and Quillen homology of modules over operads Bar constructions and Quillen homology of modules over operads

2008-02-16

arxiv.org/abs/0802.2311v4

Mathematics

Algebraic Topology

38 pages, uses xy-pic, minor revision

Scientific paper

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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