Bar constructions and Quillen homology of modules over operads

• Published in: Algebraic And Geometric Topology, vol. 10, p. 87-136
• Publication date: 2010

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.

Keywords: Model Categories ; Homotopy-Theory ; Symmetric Spectra ; Algebras ; Cohomology

Reference

• EPFL-ARTICLE-172779
• doi:10.2140/agt.2010.10.87
• View record in Web of Science

Record created on 2011-12-16, modified on 2017-05-12