Algebraic & Geometric Topology Volume 26, issue 4 (2026)

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Tautological rings of fibrations

Nils Prigge

Algebraic & Geometric Topology 26 (2026) 1565–1584

DOI: 10.2140/agt.2026.26.1565

Bibliography

1	A Berglund, Rational models for automorphisms of fiber bundles, Doc. Math. 25 (2020) 239 MR4106892
2	A Berglund, Characteristic classes for families of bundles, Selecta Math. (N.S.) 28 (2022) 51 MR4402173
3	A Berglund, I Madsen, Rational homotopy theory of automorphisms of manifolds, Acta Math. 224 (2020) 67 MR4086715
4	A Berglund, T Zeman, Algebraic models for classifying spaces of fibrations, Geom. Topol. 29 (2025) 3567 MR4974988
5	J M Boardman, Conditionally convergent spectral sequences, from: "Homotopy invariant algebraic structures" (editors J P Meyer, J Morava, W S Wilson), Contemp. Math. 239, Amer. Math. Soc. (1999) 49 MR1718076
6	A Borel, F Hirzebruch, Characteristic classes and homogeneous spaces, I, Amer. J. Math. 80 (1958) 458 MR102800
7	V Braunack-Mayer, Strict algebraic models for rational parametrised spectra, I, Algebr. Geom. Topol. 21 (2021) 917 MR4250519
8	V Braunack-Mayer, Strict algebraic models for rational parametrised spectra, I, Algebr. Geom. Topol. 21 (2021) 917 MR4250519
9	A Dold, D Puppe, Duality, trace, and transfer, from: "Proceedings of the International Conference on Geometric Topology" (editors K Borsuk, A Kirkor), PWN (1980) 81 MR656721
10	A Dress, Zur Spectralsequenz von Faserungen, Invent. Math. 3 (1967) 172 MR267585
11	Y Félix, S Halperin, J C Thomas, Rational homotopy theory, 205, Springer (2001) MR1802847
12	Y Félix, A Murillo, D Tanré, Fibrewise stable rational homotopy, J. Topol. 3 (2010) 743 MR2746336
13	Y Félix, J C Thomas, String topology on Gorenstein spaces, Math. Ann. 345 (2009) 417 MR2529482
14	S Galatius, I Grigoriev, O Randal-Williams, Tautological rings for high-dimensional manifolds, Compos. Math. 153 (2017) 851 MR3705243
15	D H Gottlieb, Poincaré duality and fibrations, Proc. Amer. Math. Soc. 76 (1979) 148 MR534407
16	I Grigoriev, Relations among characteristic classes of manifold bundles, Geom. Topol. 21 (2017) 2015 MR3654103
17	P P Grivel, Formes différentielles et suites spectrales, Ann. Inst. Fourier (Grenoble) 29 (1979) 17 MR552958
18	S Halperin, Lectures on minimal models, 9-10, Soc. Math. France (1983) 261 MR736299
19	F Hebestreit, M Land, W Lück, O Randal-Williams, A vanishing theorem for tautological classes of aspherical manifolds, Geom. Topol. 25 (2021) 47 MR4226228
20	K Kuribayashi, On the rational cohomology of the total space of the universal fibration with an elliptic fibre, from: "Homotopy theory of function spaces and related topics" (editors Y Félix, G Lupton, S B Smith), Contemp. Math. 519, Amer. Math. Soc. (2010) 165 MR2648712
21	A Lazarev, Models for classifying spaces and derived deformation theory, Proc. Lond. Math. Soc. (3) 109 (2014) 40 MR3237735
22	W Meier, Rational universal fibrations and flag manifolds, Math. Ann. 258 (1981/82) 329 MR649203
23	D Mumford, Towards an enumerative geometry of the moduli space of curves, from: "Arithmetic and geometry, II" (editors M Artin, J Tate), Progr. Math. 36, Birkhäuser (1983) 271 MR717614
24	A Murillo, The top cohomology class of certain spaces, J. Pure Appl. Algebra 84 (1993) 209 MR1201053
25	N. Prigge, On tautological classes of fibre bundles and self-embedding calculus, PhD thesis, University of Cambridge (2020)
26	N Prigge, Tautological rings of fake quaternionic spaces, Selecta Math. (N.S.) 31 (2025) 1 MR4824756
27	O Randal-Williams, Some phenomena in tautological rings of manifolds, Selecta Math. (N.S.) 24 (2018) 3835 MR3848035
28	H Shiga, M Tezuka, Rational fibrations, homogeneous spaces with positive Euler characteristics and Jacobians, Ann. Inst. Fourier (Grenoble) 37 (1987) 81 MR894562
29	B de Smit, H W Lenstra Jr., Finite complete intersection algebras and the completeness radical, J. Algebra 196 (1997) 520 MR1475123
30	J Stasheff, A classification theorem for fibre spaces, Topology 2 (1963) 239 MR154286
31	R Stoll, The stable cohomology of self-equivalences of connected sums of products of spheres, Forum Math. Sigma 12 (2024) MR4685681
32	D Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. (1977) 269 MR646078
33	D Tanré, Homotopie rationnelle : modèles de Chen, Quillen, Sullivan, 1025, Springer (1983) MR764769
34	J C Thomas, Rational homotopy of Serre fibrations, Ann. Inst. Fourier (Grenoble) 31 (1981) 71 MR638617
35	C T C Wall, Poincaré complexes, I, Ann. of Math. (2) 86 (1967) 213 MR217791