The McCord model for the tensor product of a space and a commutative ring spectrum

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dc.creatorKuhn, Nicholas J.
dc.date2002-02-05
dc.date.accessioned2026-07-07T06:35:28Z
dc.date.available2026-07-07T06:35:28Z
dc.descriptionThis paper begins by noting that, in a 1969 paper in the Transactions, M.C.McCord introduced a construction that can be interpreted as a model for the categorical tensor product of a based space and a topological abelian group. This can be adapted to Segal's very special Gamma--spaces, and then to a more modern situation: (K tensor R) where K is a based space and R is a unital, augmented, commutative, associative S--algebra. The model comes with an easy-to-describe filtration. If one lets K = S^n, and then stabilize with respect to n, one gets a filtered model for the Topological Andre--Quillen Homology of R. When R = Omega^{infty} Sigma^{infty} X, one arrives at a filtered model for the connective cover of a spectrum X, constructed from its 0th space. Another example comes by letting K be a finite complex, and R the S--dual of a finite complex Z. Dualizing again, one arrives at G.Arone's model for the Goodwillie tower of the functor sending Z to the suspension spectrum of Map(K,Z). Applying cohomology with field coefficients, one gets various spectral sequences for deloopings with known E_1--terms. A few nontrivial examples are given. In an appendix, we describe the construction for unital, commutative, associative S--algebras not necessarily augmented.
dc.descriptionAMSLatex with xypics. 22 pages
dc.identifierhttps://arxiv.org/abs/math/0202042
dc.identifierhttp://arxiv.org/abs/math/0202042
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99801
dc.subjectAlgebraic Topology
dc.subjectMathematical Physics
dc.subject55P43 (primary), 18G55 (secondary)
dc.titleThe McCord model for the tensor product of a space and a commutative ring spectrum
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