Virtual operad algebras and realization of homotopy types
Quantum Algebra
2007-05-23 v1 Algebraic Topology
Abstract
We prove that the category of algebras over a cofibrant operad admits a closed model category structure. This leads to the notion of "virtual operad algebra" - the algebra over a cofibrant resolution of the given operad. In particular, virtual commutative algebras can serve to an algebraic description of homotopy p-tipes as in the recent preprint of Mandell (electronic Hopf topology archive, october '98, see http://www.hopf.math.purdue.edu. Our main result allows one to significally simplify the proof of Mandell's theorem.
Keywords
Cite
@article{arxiv.math/9907115,
title = {Virtual operad algebras and realization of homotopy types},
author = {Vladimir Hinich},
journal= {arXiv preprint arXiv:math/9907115},
year = {2007}
}
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12 pages