Algebraic & Geometric Topology Volume 25, issue 4 (2025)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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A Quillen stability criterion for bounded cohomology

Carlos De la Cruz Mengual and Tobias Hartnick

Algebraic & Geometric Topology 25 (2025) 2317–2341

DOI: 10.2140/agt.2025.25.2317

Bibliography

1	M Bestvina, Homological stability of Aut(F_n) revisited, from: "Hyperbolic geometry and geometric group theory", Adv. Stud. Pure Math. 73, Math. Soc. Japan (2017) 1 MR3728490
2	M Bucher, M Burger, A Iozzi, The bounded Borel class and 3-manifold groups, Duke Math. J. 167 (2018) 3129 MR3874650
3	T Bühler, On the algebraic foundations of bounded cohomology, 1006, Amer. Math. Soc. (2011) MR2867320
4	M Burger, N Monod, Bounded cohomology of lattices in higher rank Lie groups, J. Eur. Math. Soc. 1 (1999) 199 MR1694584
5	M Burger, N Monod, On and around the bounded cohomology of SL₂, from: "Rigidity in dynamics and geometry" (editors M Burger, A Iozzi), Springer (2002) 19 MR1919394
6	C De la Cruz Mengual, On bounded-cohomological stability for classical groups, PhD thesis, ETH Zürich (2019)
7	C De la Cruz Mengual, The degree-three bounded cohomology of complex Lie groups of classical type, preprint (2023) arXiv:2304.00607
8	C De la Cruz Mengual, T Hartnick, Stabilization of bounded cohomology for classical groups, preprint (2022) arXiv:2201.03879
9	J Essert, Homological stability for classical groups, Israel J. Math. 198 (2013) 169 MR3096635
10	R Frigerio, Bounded cohomology of discrete groups, 227, Amer. Math. Soc. (2017) MR3726870
11	M Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. 56 (1982) 5 MR686042
12	J L Harer, Stability of the homology of the mapping class groups of orientable surfaces, Ann. of Math. 121 (1985) 215 MR786348
13	A Hatcher, K Vogtmann, Homology stability for outer automorphism groups of free groups, Algebr. Geom. Topol. 4 (2004) 1253 MR2113904
14	W van der Kallen, Homology stability for linear groups, Invent. Math. 60 (1980) 269 MR586429
15	J McCleary, A user’s guide to spectral sequences, 58, Cambridge Univ. Press (2001) MR1793722
16	N Monod, Continuous bounded cohomology of locally compact groups, 1758, Springer (2001) MR1840942
17	N Monod, Stabilization for SL_n in bounded cohomology, from: "Discrete geometric analysis", Contemp. Math. 347, Amer. Math. Soc. (2004) 191 MR2077038
18	N Monod, Vanishing up to the rank in bounded cohomology, Math. Res. Lett. 14 (2007) 681 MR2335993
19	N Monod, S Nariman, Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups, Invent. Math. 232 (2023) 1439 MR4588567
20	V L Popov, Generically multiple transitive algebraic group actions, from: "Algebraic groups and homogeneous spaces", Tata Inst. Fund. Res. Stud. Math. 19, Tata Inst. Fund. Res. (2007) 481 MR2348915
21	D Quillen, Notebook 1974-1, personal notes (1974)
22	D Sprehn, N Wahl, Homological stability for classical groups, Trans. Amer. Math. Soc. 373 (2020) 4807 MR4127863
23	K Vogtmann, A Stiefel complex for the orthogonal group of a field, Comment. Math. Helv. 57 (1982) 11 MR672842
24	C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324
25	R J Zimmer, Ergodic theory and semisimple groups, 81, Birkhäuser (1984) MR776417