Algebraic & Geometric Topology Volume 22, issue 1 (2022)

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The rank filtration via a filtered bar construction

Gregory Arone and Kathryn Lesh

Algebraic & Geometric Topology 22 (2022) 251–306

DOI: 10.2140/agt.2022.22.251

Bibliography

1	G Z Arone, W G Dwyer, Partition complexes, Tits buildings and symmetric products, Proc. Lond. Math. Soc. 82 (2001) 229 MR1794263
2	G Z Arone, W G Dwyer, K Lesh, Bredon homology of partition complexes, Doc. Math. 21 (2016) 1227 MR3578208
3	G Arone, W G Dwyer, K Lesh, p–toral approximations compute Bredon homology, Int. Math. Res. Not. 2021 (2021) 3822 MR4227586
4	G Arone, K Lesh, Filtered spectra arising from permutative categories, J. Reine Angew. Math. 604 (2007) 73 MR2320314
5	G Z Arone, K Lesh, Augmented Γ–spaces, the stable rank filtration, and a bu analogue of the Whitehead conjecture, Fund. Math. 207 (2010) 29 MR2576278
6	A K Bousfield, E M Friedlander, Homotopy theory of Γ–spaces, spectra, and bisimplicial sets, from: "Geometric applications of homotopy theory, II" (editors M G Barratt, M E Mahowald), Lecture Notes in Math. 658, Springer (1978) 80 MR513569
7	T G Goodwillie, Calculus, I : The first derivative of pseudoisotopy theory, K–Theory 4 (1990) 1 MR1076523
8	N J Kuhn, A Kahn–Priddy sequence and a conjecture of G W Whitehead, Math. Proc. Cambridge Philos. Soc. 92 (1982) 467 MR677471
9	N J Kuhn, S B Priddy, The transfer and Whitehead’s conjecture, Math. Proc. Cambridge Philos. Soc. 98 (1985) 459 MR803606
10	M Lydakis, Smash products and Γ–spaces, Math. Proc. Cambridge Philos. Soc. 126 (1999) 311 MR1670245
11	M A Mandell, An inverse K–theory functor, Doc. Math. 15 (2010) 765 MR2735988
12	J P May, The geometry of iterated loop spaces, 271, Springer (1972) MR0420610
13	E Riehl, Categorical homotopy theory, 24, Cambridge Univ. Press (2014) MR3221774
14	J Rognes, A spectrum level rank filtration in algebraic K–theory, Topology 31 (1992) 813 MR1191383
15	G Segal, Categories and cohomology theories, Topology 13 (1974) 293 MR353298