Applications and generalizations of the approximation theorem

May, J. P.

doi:10.1007/bfb0088077

Cited by 5 publications

(6 citation statements)

References 41 publications

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“…between loop spaces. As observed in [16], such comparisons are quite trivial verifications in view of the very simple and explicit nature of the maps g" and an. To define the model level analogs of loop sums and smash products, and for other purposes, we first note that A has sums and products, and then introduce notions of additive and multiplicative pairings of coefficient systems.…”

Section: ¡5»0 'mentioning

confidence: 99%

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James Maps, Segal Maps, and the Kahn-Priddy Theorem

Caruso¹,

Cohen²,

May³

et al. 1984

Transactions of the American Mathematical Society

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Section: ¡5»0 'mentioning

confidence: 99%

“…Proofs of the above statements may be found in [16,5,20 and 4]; they need not concern us here. What does concern us is how these maps relate to various standard maps (loop sums, smash products, etc.)…”

Section: ¡5»0 'mentioning

confidence: 99%

James Maps, Segal Maps, and the Kahn-Priddy Theorem

Caruso¹,

Cohen²,

May³

et al. 1984

Transactions of the American Mathematical Society

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“…Additive iterated and infinite loop space theory This includes operads, the two-sided bar construction of monads, iterated and infinite loop space theory via operads [7], [12], [18], [28], [29], homology of iterated and infinite loop spaces [11], [17], [39] the work on classifying spaces and fibrations [15], on spectra associated with permutative categories [13], [23], and the joint work of May and Thomason on uniqueness of infinite loop space machines [22], [32].…”

Section: Prefacementioning

confidence: 99%

Homotopy Methods in Algebraic Topology

Greenlees¹,

Bruner²,

Kuhn³

2001

Contemporary Mathematics

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“…This structure leads (in [12]) to simple combinatorial approximations to spaces of the form QP^ÏPX. Mahowald [11] found a remarkable way to exploit this structure to construct infinite families of elements in the stable homotopy groups of spheres.…”

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“…That is, given a suitably structured space X, one can manufacture "deloopings" B n X and equivalences between X and Q"B n X. There are three main machines for carrying out this program, due to Boardman and Vogt, Segal, and myself [3], [22], [12]. All three may be viewed as exercises in topological algebra, the study of algebraic structure on topological spaces.…”

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confidence: 99%