Virtual operad algebras and realization of homotopy types

Details Virtual operad algebras and realization of homotopy types Virtual operad algebras and realization of homotopy types

1999-07-19

arxiv.org/abs/math/9907115v1

Mathematics

Quantum Algebra

12 pages

Scientific paper

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.

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