2018
DOI: 10.48550/arxiv.1805.07184
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Cellular $E_k$-algebras

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.

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Cited by 11 publications
(14 citation statements)
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“…Recently Galatius, Kupers and Randal-Williams [GKRW18] identified and proved a new kind of stabilization result, which they describe by the slogan "the failure of homological stability is itself stable". They defined homological-degree-shifting stabilization maps and use them to prove secondary homological stability for the homology of mapping class groups and general linear groups outside the stable range of (primary) homological stability.…”
Section: Current Research Directionsmentioning
confidence: 99%
“…Recently Galatius, Kupers and Randal-Williams [GKRW18] identified and proved a new kind of stabilization result, which they describe by the slogan "the failure of homological stability is itself stable". They defined homological-degree-shifting stabilization maps and use them to prove secondary homological stability for the homology of mapping class groups and general linear groups outside the stable range of (primary) homological stability.…”
Section: Current Research Directionsmentioning
confidence: 99%
“…(1) Though Galatius, Kupers, and I have recently proposed another [GKRW18a], which in fortunate circumstances can provide information beyond classical homological stability, for example in the case of mapping class groups of surfaces [GKRW18b].…”
Section: The Cohen-lenstra Heuristic For Function Fieldsmentioning
confidence: 99%
“…In this exposition of [EVW16] I will present their argument differently to the way it appears in that paper, closer to the framework of [GKRW18a] than to the classical approach to homological stability described above. While many of the key steps are unchanged, I find that this streamlined argument clarifies the essential points.…”
Section: Introductionmentioning
confidence: 98%
“…TQ-homology and its relative form, topological Andre-Quillen (TAQ) homology, first introduced in [4] for commutative ring spectra (see also [3,5,6,21,35,38,39,45]), are defined as derived indecomposables of O-algebras analogous to Quillen homology of commutative algebras [1,44]; see also [19,24,20,41]. More precisely, factoring the canonical truncation map O → τ 1 O (see [28]) in the category of operads as O → J → τ 1 O, a cofibration followed by a weak equivalence, we get the corresponding change of operads adjunction…”
Section: Tq-local O-algebras and Tq| Nilm -Resolutionsmentioning
confidence: 99%