Geometry & Topology Volume 29, issue 7 (2025)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Algebraic models for classifying spaces of fibrations

Alexander Berglund and Tomáš Zeman

Geometry & Topology 29 (2025) 3567–3634

DOI: 10.2140/gt.2025.29.3567

Bibliography

1	J Bajpai, G Harder, I Horozov, M V Moya Giusti, Boundary and Eisenstein cohomology of SL₃(ℤ), Math. Ann. 377 (2020) 199 MR4099634
2	W D Barcus, M G Barratt, On the homotopy classification of the extensions of a fixed map, Trans. Amer. Math. Soc. 88 (1958) 57 MR97060
3	D Barden, Simply connected five-manifolds, Ann. of Math. 82 (1965) 365 MR184241
4	H Bass, J Milnor, J P Serre, Solution of the congruence subgroup problem for SL_n(n ≥ 3) and Sp_2n (n ≥ 2), Inst. Hautes Études Sci. Publ. Math. 33 (1967) 59 MR244257
5	S Basu, F T Farrell, Realizing congruence subgroups inside the diffeomorphism group of a product of homotopy spheres, Topology Appl. 202 (2016) 205 MR3464161
6	H J Baues, On the group of homotopy equivalences of a manifold, Trans. Amer. Math. Soc. 348 (1996) 4737 MR1340168
7	H J Baues, J Buth, On the group of homotopy equivalences of simply connected five manifolds, Math. Z. 222 (1996) 573 MR1406269
8	H J Baues, J M Lemaire, Minimal models in homotopy theory, Math. Ann. 225 (1977) 219 MR431172
9	A Berglund, Homological perturbation theory for algebras over operads, Algebr. Geom. Topol. 14 (2014) 2511 MR3276839
10	A Berglund, Rational homotopy theory of mapping spaces via Lie theory for L_∞-algebras, Homology Homotopy Appl. 17 (2015) 343 MR3431305
11	A Berglund, Rational models for automorphisms of fiber bundles, Doc. Math. 25 (2020) 239 MR4106892
12	A Berglund, Characteristic classes for families of bundles, Selecta Math. 28 (2022) 51 MR4402173
13	A Berglund, On exponential groups and Maurer–Cartan spaces, Proc. Amer. Math. Soc. Ser. B 11 (2024) 358 MR4771859
14	A Berglund, J Bergström, Hirzebruch L-polynomials and multiple zeta values, Math. Ann. 372 (2018) 125 MR3856808
15	A Berglund, I Madsen, Homological stability of diffeomorphism groups, Pure Appl. Math. Q. 9 (2013) 1 MR3126499
16	A Berglund, I Madsen, Rational homotopy theory of automorphisms of manifolds, Acta Math. 224 (2020) 67 MR4086715
17	J Block, A Lazarev, André–Quillen cohomology and rational homotopy of function spaces, Adv. Math. 193 (2005) 18 MR2132759
18	A Borel, Density and maximality of arithmetic subgroups, J. Reine Angew. Math. 224 (1966) 78 MR205999
19	A Borel, Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. 7 (1974) 235 MR387496
20	A Borel, Stable real cohomology of arithmetic groups, II, from: "Manifolds and Lie groups" (editors S Murakami, J Hano, K Okamoto, A Morimoto, H Ozeki), Progr. Math. 14, Birkhäuser (1981) 21 MR642850
21	A Borel, J P Serre, Corners and arithmetic groups, Comment. Math. Helv. 48 (1973) 436 MR387495
22	A K Bousfield, The localization of spaces with respect to homology, Topology 14 (1975) 133 MR380779
23	A K Bousfield, V K A M Gugenheim, On PL de Rham theory and rational homotopy type, 179, Amer. Math. Soc. (1976) MR425956
24	A K Bousfield, D M Kan, Homotopy limits, completions and localizations, 304, Springer (1972) MR365573
25	K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
26	D Burghelea, Rational homotopy theory, group actions and algebraic K-theory of topological spaces, from: "Algebraic homotopy and local algebra" (editors J M Lemaire, J C Thomas), Astérisque 113-114, Soc. Math. France (1984) 60 MR749043
27	D Crowley, J Nordström, The classification of 2-connected 7-manifolds, Proc. Lond. Math. Soc. 119 (2019) 1 MR3957830
28	H Derksen, G Kemper, Computational invariant theory, 130, Springer (2002) MR1918599
29	F Diamond, J Shurman, A first course in modular forms, 228, Springer (2005) MR2112196
30	E Dror, W G Dwyer, D M Kan, An arithmetic square for virtually nilpotent spaces, Illinois J. Math. 21 (1977) 242 MR438330
31	E Dror, W G Dwyer, D M Kan, Self-homotopy equivalences of virtually nilpotent spaces, Comment. Math. Helv. 56 (1981) 599 MR656214
32	E Dror, A Zabrodsky, Unipotency and nilpotency in homotopy equivalences, Topology 18 (1979) 187 MR546789
33	Y Félix, M Fuentes, A Murillo, Lie models of homotopy automorphism monoids and classifying fibrations, Adv. Math. 402 (2022) 108359 MR4401825
34	Y Félix, S Halperin, J C Thomas, Rational homotopy theory, 205, Springer (2001) MR1802847
35	A Floer, Klassifikation hochzusammenhängender Poincaré-Räume, master’s thesis, Ruhr-Universität Bochum (1982)
36	M Furusawa, M Tezuka, N Yagita, On the cohomology of classifying spaces of torus bundles and automorphic forms, J. London Math. Soc. 37 (1988) 520 MR939127
37	S Galatius, O Randal-Williams, Stable moduli spaces of high-dimensional manifolds, Acta Math. 212 (2014) 257 MR3207759
38	P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
39	A Gómez-Tato, S Halperin, D Tanré, Rational homotopy theory for non-simply connected spaces, Trans. Amer. Math. Soc. 352 (2000) 1493 MR1653355
40	M Grey, On rational homological stability for block automorphisms of connected sums of products of spheres, Algebr. Geom. Topol. 19 (2019) 3359 MR4045356
41	R Hain, Infinitesimal presentations of the Torelli groups, J. Amer. Math. Soc. 10 (1997) 597 MR1431828
42	S Halperin, Lectures on minimal models, 9-10, Soc. Math. France (1983) 261 MR736299
43	P Hilton, On G-spaces, Bol. Soc. Brasil. Mat. 7 (1976) 65 MR488048
44	P Hilton, G Mislin, J Roitberg, Localization of nilpotent groups and spaces, 15, North-Holland (1975) MR478146
45	G Hochschild, Introduction to affine algebraic groups, Holden-Day (1971) MR277535
46	M A Kervaire, J W Milnor, Groups of homotopy spheres, I, Ann. of Math. 77 (1963) 504 MR148075
47	G Köhler, Theta series on the theta group, Abh. Math. Sem. Univ. Hamburg 58 (1988) 15 MR1027431
48	A Kupers, J Miller, P Patzt, Improved homological stability for certain general linear groups, Proc. Lond. Math. Soc. 125 (2022) 511 MR4480882
49	A Kupers, O Randal-Williams, The cohomology of Torelli groups is algebraic, Forum Math. Sigma 8 (2020) MR4190064
50	A Lazarev, Models for classifying spaces and derived deformation theory, Proc. Lond. Math. Soc. 109 (2014) 40 MR3237735
51	L A Lucas, O Saeki, Diffeomorphisms of a product of spheres and embedded spheres, Topology Appl. 123 (2002) 471 MR1924046
52	J Maunder, Unbased rational homotopy theory: a Lie algebra approach, preprint (2015) arXiv:1511.07669
53	J P May, Classifying spaces and fibrations, 155, Amer. Math. Soc. (1975) MR370579
54	J P May, Equivariant homotopy and cohomology theory, 91, Amer. Math. Soc. (1996) MR1413302
55	J S Milne, Algebraic groups: the theory of group schemes of finite type over a field, 170, Cambridge Univ. Press (2017) MR3729270
56	S Morita, Characteristic classes of T²-bundles, from: "Homotopy theory and related topics" (editor H Toda), Adv. Stud. Pure Math. 9, North-Holland (1987) 135 MR896950
57	J F Oprea, Lifting homotopy actions in rational homotopy theory, J. Pure Appl. Algebra 32 (1984) 177 MR741964
58	A Putman, A new approach to twisted homological stability with applications to congruence subgroups, J. Topol. 16 (2023) 1315 MR4671766
59	D Quillen, Rational homotopy theory, Ann. of Math. 90 (1969) 205 MR258031
60	B Saleh, Algebraic groups of homotopy classes of automorphisms and operadic Koszul duality, preprint (2023) arXiv:2305.02076
61	D Segal, Polycyclic groups, 82, Cambridge Univ. Press (1983) MR713786
62	J P Serre, Arithmetic groups, from: "Homological group theory" (editor C T C Wall), London Math. Soc. Lecture Note Ser. 36, Cambridge Univ. Press (1979) 105 MR564421
63	A J Sieradski, Stabilization of self-equivalences of the pseudoprojective spaces, Michigan Math. J. 19 (1972) 109 MR300280
64	L Smith, Polynomial invariants of finite groups, 6, A K Peters (1995) MR1328644
65	R Stoll, The stable cohomology of self-equivalences of connected sums of products of spheres, Forum Math. Sigma 12 (2024) MR4685681
66	D Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. 47 (1977) 269 MR646078
67	D Tanré, Homotopie rationnelle : modèles de Chen, Quillen, Sullivan, 1025, Springer (1983) MR764769
68	G Triantafillou, The arithmeticity of groups of automorphisms of spaces, from: "Tel Aviv Topology Conference : Rothenberg Festschrift" (editors M Farber, W Lück, S Weinberger), Contemp. Math. 231, Amer. Math. Soc. (1999) 283 MR1707350
69	C T C Wall, Classification problems in differential topology, VI : Classification of (s−1)-connected (2s+1)-manifolds, Topology 6 (1967) 273 MR216510
70	G Wiese, Computational arithmetic of modular forms, from: "Notes from the International Autumn School on Computational Number Theory" (editors I Inam, E Büyükaşık), Springer (2019) 63 MR3932019
71	C W Wilkerson, Applications of minimal simplicial groups, Topology 15 (1976) 111 MR402737