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On the mod-$\ell$ homology of the classifying space for commutativity

Cihan Okay and Ben Williams

Algebraic & Geometric Topology 20 (2020) 883–923
Bibliography
1 A Adem, F R Cohen, E Torres Giese, Commuting elements, simplicial spaces and filtrations of classifying spaces, Math. Proc. Cambridge Philos. Soc. 152 (2012) 91 MR2860418
2 A Adem, J M Gómez, A classifying space for commutativity in Lie groups, Algebr. Geom. Topol. 15 (2015) 493 MR3325746
3 A Adem, J M Gómez, J A Lind, U Tillmann, Infinite loop spaces and nilpotent K–theory, Algebr. Geom. Topol. 17 (2017) 869 MR3623675
4 O Antolín-Camarena, S Gritschacher, B Villarreal, Classifying spaces for commutativity of low-dimensional Lie groups, preprint (2018) arXiv:1802.03632
5 F Borceux, Handbook of categorical algebra, I: Basic category theory, 50, Cambridge Univ. Press (1994) MR1291599
6 A K Bousfield, D M Kan, Homotopy limits, completions and localizations, 304, Springer (1972) MR0365573
7 M R Bridson, P de la Harpe, V Kleptsyn, The Chabauty space of closed subgroups of the three-dimensional Heisenberg group, Pacific J. Math. 240 (2009) 1 MR2485473
8 C Broto, N Kitchloo, Classifying spaces of Kac–Moody groups, Math. Z. 240 (2002) 621 MR1924024
9 G Carlsson, Equivariant stable homotopy and Sullivan’s conjecture, Invent. Math. 103 (1991) 497 MR1091616
10 W G Dwyer, C W Wilkerson, Homotopy fixed-point methods for Lie groups and finite loop spaces, Ann. of Math. 139 (1994) 395 MR1274096
11 W Dwyer, A Zabrodsky, Maps between classifying spaces, from: "Algebraic topology" (editors J Aguadé, R Kane), Lecture Notes in Math. 1298, Springer (1987) 106 MR928826
12 E M Friedlander, Exceptional isogenies and the classifying spaces of simple Lie groups, Ann. Math. 101 (1975) 510 MR0391078
13 E M Friedlander, G Mislin, Cohomology of classifying spaces of complex Lie groups and related discrete groups, Comment. Math. Helv. 59 (1984) 347 MR761803
14 E M Friedlander, G Mislin, Locally finite approximation of Lie groups, I, Invent. Math. 83 (1986) 425 MR827361
15 E M Friedlander, G Mislin, Conjugacy classes of finite solvable subgroups in Lie groups, Ann. Sci. École Norm. Sup. 21 (1988) 179 MR956765
16 S P Gritschacher, The spectrum for commutative complex K–theory, Algebr. Geom. Topol. 18 (2018) 1205 MR3773753
17 H Hironaka, Triangulations of algebraic sets, from: "Algebraic geometry" (editor R Hartshorne), Proc. Sympos. Pure Math. 29, Amer. Math. Soc. (1975) 165 MR0374131
18 P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
19 J Hollender, R M Vogt, Modules of topological spaces, applications to homotopy limits and E structures, Arch. Math. (Basel) 59 (1992) 115 MR1170635
20 J C Jantzen, Representations of algebraic groups, 131, Academic (1987) MR899071
21 J A Lind, Diagram spaces, diagram spectra and spectra of units, Algebr. Geom. Topol. 13 (2013) 1857 MR3073903
22 A Lubotzky, A R Magid, Varieties of representations of finitely generated groups, 336, Amer. Math. Soc. (1985) MR818915
23 J P May, K Ponto, More concise algebraic topology: localization, completion, and model categories, Univ. of Chicago Press (2012) MR2884233
24 J P Meyer, Bar and cobar constructions, II, J. Pure Appl. Algebra 43 (1986) 179 MR866618
25 C Okay, Homotopy colimits of classifying spaces of abelian subgroups of a finite group, Algebr. Geom. Topol. 14 (2014) 2223 MR3331614
26 C Okay, Colimits of abelian groups, J. Algebra 443 (2015) 1 MR3400392
27 C Okay, Spherical posets from commuting elements, J. Group Theory 21 (2018) 593 MR3819543
28 D Quillen, The spectrum of an equivariant cohomology ring, I, Ann. of Math. 94 (1971) 549 MR298694
29 G Segal, Categories and cohomology theories, Topology 13 (1974) 293 MR353298
30 A Strøm, The homotopy category is a homotopy category, Arch. Math. (Basel) 23 (1972) 435 MR321082
31 E Torres Giese, D Sjerve, Fundamental groups of commuting elements in Lie groups, Bull. Lond. Math. Soc. 40 (2008) 65 MR2409179
32 B Villarreal, Cosimplicial groups and spaces of homomorphisms, Algebr. Geom. Topol. 17 (2017) 3519 MR3709654