Cellular $E_k$-algebras

Søren Galatius, Alexander Kupers, Oscar Randal-Williams

Abstract: We give a set of foundations for cellular

E_{k}

-algebras which are especially convenient for applications to homological stability. We provide conceptual and computational tools in this setting, such as filtrations, a homology theory for

E_{k}

-algebras with a Hurewicz theorem, CW approximations, and many spectral sequences, which shall be used for such applications in future papers.

Mathematics Subject Classification ID

Topological quantum field theories (aspects of differential topology) (57R56) Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) (57R15) Other types of cobordism (57R90) Infinite loop spaces (55P47)

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