Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
The space of nonextendable quasimorphisms

Morimichi Kawasaki, Mitsuaki Kimura, Shuhei Maruyama, Takahiro Matsushita and Masato Mimura
Algebraic & Geometric Topology 25 (2025) 1169–1226
DOI: 10.2140/agt.2025.25.1169
Bibliography
1 T Akita, Y Liu, Second mod 2 homology of Artin groups, Algebr. Geom. Topol. 18 (2018) 547 MR3748252
2 U Bader, A Lubotzky, R Sauer, S Weinberger, Stability and instability of lattices in semisimple groups, J. Anal. Math. 151 (2023) 1 MR4682943
3 U Bader, R Sauer, Higher Kazhdan property and unitary cohomology of arithmetic groups, preprint (2023) arXiv:2308.06517
4 A Banyaga, Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique, Comment. Math. Helv. 53 (1978) 174 MR490874
5 A Banyaga, The structure of classical diffeomorphism groups, 400, Kluwer (1997) MR1445290
6 C Bavard, Longueur stable des commutateurs, Enseign. Math. 37 (1991) 109 MR1115747
7 B Bekka, P de la Harpe, Unitary representations of groups, duals, and characters, 250, Amer. Math. Soc. (2020) MR4249450
8 B Bekka, P de la Harpe, A Valette, Kazhdan’s property (T), 11, Cambridge Univ. Press (2008) MR2415834
9 M Bestvina, K Bromberg, K Fujiwara, Bounded cohomology with coefficients in uniformly convex Banach spaces, Comment. Math. Helv. 91 (2016) 203 MR3493369
10 M Bestvina, K Bromberg, K Fujiwara, Stable commutator length on mapping class groups, Ann. Inst. Fourier (Grenoble) 66 (2016) 871 MR3494163
11 M Bestvina, M Feighn, A combination theorem for negatively curved groups, J. Differential Geom. 35 (1992) 85 MR1152226
12 M Bestvina, K Fujiwara, Bounded cohomology of subgroups of mapping class groups, Geom. Topol. 6 (2002) 69 MR1914565
13 R Bieri, Mayer–Vietoris sequences for HNN-groups and homological duality, Math. Z. 143 (1975) 123 MR382404
14 A Borel, Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. 7 (1974) 235 MR387496
15 A Borel, Stable and L2-cohomology of arithmetic groups, Bull. Amer. Math. Soc. 3 (1980) 1025 MR585182
16 A Borel, Stable real cohomology of arithmetic groups, II, from: "Manifolds and Lie groups", Progr. Math. 14, Birkhäuser (1981) 21 MR642850
17 J Bowden, S W Hensel, R Webb, Quasi-morphisms on surface diffeomorphism groups, J. Amer. Math. Soc. 35 (2022) 211 MR4322392
18 M Brandenbursky, J Kędra, Fragmentation norm and relative quasimorphisms, Proc. Amer. Math. Soc. 150 (2022) 4519 MR4470192
19 K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
20 M Bucher, N Monod, The bounded cohomology of SL2 over local fields and S-integers, Int. Math. Res. Not. 2019 (2019) 1601 MR3932589
21 D Burago, S Ivanov, L Polterovich, Conjugation-invariant norms on groups of geometric origin, from: "Groups of diffeomorphisms", Adv. Stud. Pure Math. 52, Math. Soc. Japan (2008) 221 MR2509711
22 M Burger, N Monod, Bounded cohomology of lattices in higher rank Lie groups, J. Eur. Math. Soc. 1 (1999) 199 MR1694584
23 M Burger, N Monod, Continuous bounded cohomology and applications to rigidity theory, Geom. Funct. Anal. 12 (2002) 219 MR1911660
24 M Burger, S Mozes, Finitely presented simple groups and products of trees, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997) 747 MR1446574
25 D Calegari, Circular groups, planar groups, and the Euler class, from: "Proceedings of the Casson Fest", Geom. Topol. Monogr. 7, Geom. Topol. Publ. (2004) 431 MR2172491
26 D Calegari, scl, 20, Math. Soc. Japan (2009) MR2527432
27 D Calegari, N Monden, M Sato, On stable commutator length in hyperelliptic mapping class groups, Pacific J. Math. 272 (2014) 323 MR3284890
28 P Capovilla, C Löh, M Moraschini, Amenable category and complexity, Algebr. Geom. Topol. 22 (2022) 1417 MR4474790
29 T D Cochran, S Harvey, P D Horn, Higher-order signature cocycles for subgroups of mapping class groups and homology cylinders, Int. Math. Res. Not. 2012 (2012) 3311 MR2946227
30 M De Chiffre, L Glebsky, A Lubotzky, A Thom, Stability, cohomology vanishing, and nonapproximable groups, Forum Math. Sigma 8 (2020) MR4080477
31 K Dekimpe, M Hartl, S Wauters, A seven-term exact sequence for the cohomology of a group extension, J. Algebra 369 (2012) 70 MR2959787
32 H Endo, D Kotschick, Bounded cohomology and non-uniform perfection of mapping class groups, Invent. Math. 144 (2001) 169 MR1821147
33 M Entov, L Polterovich, Quasi-states and symplectic intersections, Comment. Math. Helv. 81 (2006) 75 MR2208798
34 D B A Epstein, K Fujiwara, The second bounded cohomology of word-hyperbolic groups, Topology 36 (1997) 1275 MR1452851
35 A Fathi, Structure of the group of homeomorphisms preserving a good measure on a compact manifold, Ann. Sci. École Norm. Sup. 13 (1980) 45 MR584082
36 F Fournier-Facio, Y Lodha, Second bounded cohomology of groups acting on 1-manifolds and applications to spectrum problems, Adv. Math. 428 (2023) 109162 MR4604795
37 F Fournier-Facio, C Löh, M Moraschini, Bounded cohomology and binate groups, J. Aust. Math. Soc. 115 (2023) 204 MR4640119
38 F Fournier-Facio, C Löh, M Moraschini, Bounded cohomology of finitely presented groups: vanishing, non-vanishing, and computability, Ann. Sc. Norm. Super. Pisa Cl. Sci. 25 (2024) 1169 MR4778473
39 F Fournier-Facio, R D Wade, Aut-invariant quasimorphisms on groups, Trans. Amer. Math. Soc. 376 (2023) 7307 MR4636691
40 R Frigerio, Bounded cohomology of discrete groups, 227, Amer. Math. Soc. (2017) MR3726870
41 R Frigerio, M B Pozzetti, A Sisto, Extending higher-dimensional quasi-cocycles, J. Topol. 8 (2015) 1123 MR3431671
42 K Fujiwara, T Soma, Bounded classes in the cohomology of manifolds, Geom. Dedicata 92 (2002) 73 MR1934011
43 S M Gersten, A presentation for the special automorphism group of a free group, J. Pure Appl. Algebra 33 (1984) 269 MR761633
44 L Glebsky, A Lubotzky, N Monod, B Rangarajan, Asymptotic cohomology and uniform stability for lattices in semisimple groups, preprint (2023) arXiv:2301.00476
45 M Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. 56 (1982) 5 MR686042
46 M Gromov, Hyperbolic groups, from: "Essays in group theory", Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
47 R Hain, Infinitesimal presentations of the Torelli groups, J. Amer. Math. Soc. 10 (1997) 597 MR1431828
48 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
49 M Hull, D Osin, Induced quasicocycles on groups with hyperbolically embedded subgroups, Algebr. Geom. Topol. 13 (2013) 2635 MR3116299
50 T Ishida, Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-disk, PhD thesis, University of Tokyo (2013)
51 T Ishida, Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-disk via braid groups, Proc. Amer. Math. Soc. Ser. B 1 (2014) 43 MR3181631
52 T Ishida, Homomorphisms on groups of volume-preserving diffeomorphisms via fundamental groups, from: "Geometry, dynamics, and foliations", Adv. Stud. Pure Math. 72, Math. Soc. Japan (2017) 387 MR3726720
53 N V Ivanov, Leray theorems in bounded cohomology theory, preprint (2020) arXiv:2012.08038
54 M Kaluba, D Kielak, P W Nowak, On property (T) for Aut(Fn) and SLn(ℤ), Ann. of Math. 193 (2021) 539 MR4224715
55 M Kaluba, P W Nowak, N Ozawa, Aut(𝔽5) has property (T), Math. Ann. 375 (2019) 1169 MR4023374
56 M Kawasaki, Relative quasimorphisms and stably unbounded norms on the group of symplectomorphisms of the Euclidean spaces, J. Symplectic Geom. 14 (2016) 297 MR3523258
57 M Kawasaki, Bavard’s duality theorem on conjugation-invariant norms, Pacific J. Math. 288 (2017) 157 MR3667767
58 M Kawasaki, M Kimura, Ĝ-invariant quasimorphisms and symplectic geometry of surfaces, Israel J. Math. 247 (2022) 845 MR4425357
59 M Kawasaki, M Kimura, S Maruyama, T Matsushita, M Mimura, Coarse group theoretic study on stable mixed commutator length, preprint (2023) arXiv:2306.08618
60 M Kawasaki, M Kimura, T Matsushita, M Mimura, Bavard’s duality theorem for mixed commutator length, Enseign. Math. 68 (2022) 441 MR4452430
61 M Kawasaki, M Kimura, T Matsushita, M Mimura, Commuting symplectomorphisms on a surface and the flux homomorphism, Geom. Funct. Anal. 33 (2023) 1322 MR4646410
62 M Kawasaki, S Maruyama, On boundedness of characteristic class via quasi-morphism, J. Topol. Anal. (2024)
63 J Kędra, D Kotschick, S Morita, Crossed flux homomorphisms and vanishing theorems for flux groups, Geom. Funct. Anal. 16 (2006) 1246 MR2276539
64 M Kimura, Conjugation-invariant norms on the commutator subgroup of the infinite braid group, J. Topol. Anal. 10 (2018) 471 MR3809596
65 D Kotschick, S Morita, Characteristic classes of foliated surface bundles with area-preserving holonomy, J. Differential Geom. 75 (2007) 273 MR2286823
66 K Li, Bounded cohomology of classifying spaces for families of subgroups, Algebr. Geom. Topol. 23 (2023) 933 MR4587321
67 A V Malyutin, Operators in the spaces of pseudocharacters of braid groups, Algebra i Analiz 21 (2009) 136 MR2553045
68 K Mann, Unboundedness of some higher Euler classes, Algebr. Geom. Topol. 20 (2020) 1221 MR4105551
69 S Maruyama, T Matsushita, M Mimura, Invariant quasimorphisms for groups acting on the circle and non-equivalence of SCL, (2022) arXiv:2203.09221
70 S Matsumoto, S Morita, Bounded cohomology of certain groups of homeomorphisms, Proc. Amer. Math. Soc. 94 (1985) 539 MR787909
71 J McCool, A faithful polynomial representation of OutF3, Math. Proc. Cambridge Philos. Soc. 106 (1989) 207 MR1002533
72 J Milnor, Introduction to algebraic K-theory, 72, Princeton Univ. Press (1971) MR349811
73 I Mineyev, Straightening and bounded cohomology of hyperbolic groups, Geom. Funct. Anal. 11 (2001) 807 MR1866802
74 N Monod, Continuous bounded cohomology of locally compact groups, 1758, Springer (2001) MR1840942
75 N Monod, Stabilization for SLn in bounded cohomology, from: "Discrete geometric analysis", Contemp. Math. 347, Amer. Math. Soc. (2004) 191 MR2077038
76 N Monod, Vanishing up to the rank in bounded cohomology, Math. Res. Lett. 14 (2007) 681 MR2335993
77 N Monod, On the bounded cohomology of semi-simple groups, S-arithmetic groups and products, J. Reine Angew. Math. 640 (2010) 167 MR2629693
78 N Monod, Lamplighters and the bounded cohomology of Thompson’s group, Geom. Funct. Anal. 32 (2022) 662 MR4431125
79 N Monod, S Nariman, Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups, Invent. Math. 232 (2023) 1439 MR4588567
80 N Monod, Y Shalom, Cocycle superrigidity and bounded cohomology for negatively curved spaces, J. Differential Geom. 67 (2004) 395 MR2153026
81 A Monzner, N Vichery, F Zapolsky, Partial quasimorphisms and quasistates on cotangent bundles, and symplectic homogenization, J. Mod. Dyn. 6 (2012) 205 MR2968955
82 M Moraschini, G Raptis, Amenability and acyclicity in bounded cohomology, Rev. Mat. Iberoam. 39 (2023) 2371 MR4671438
83 J Neukirch, A Schmidt, K Wingberg, Cohomology of number fields, 323, Springer (2008) MR2392026
84 W D Neumann, L Reeves, Central extensions of word hyperbolic groups, Ann. of Math. 145 (1997) 183 MR1432040
85 B B Newman, Some results on one-relator groups, Bull. Amer. Math. Soc. 74 (1968) 568 MR222152
86 M Nitsche, Computer proofs for property (T), and SDP duality, preprint (2020) arXiv:2009.05134
87 L Polterovich, The geometry of the group of symplectic diffeomorphisms, Birkhäuser (2001) MR1826128
88 L Polterovich, D Rosen, Function theory on symplectic manifolds, 34, Amer. Math. Soc. (2014) MR3241729
89 P Py, Quasi-morphismes et invariant de Calabi, Ann. Sci. École Norm. Sup. 39 (2006) 177 MR2224660
90 A I Shtern, Extension of pseudocharacters from normal subgroups, III, Proc. Jangjeon Math. Soc. 19 (2016) 609 MR3618452
91 W Thurston, Noncobordant foliations of S3, Bull. Amer. Math. Soc. 78 (1972) 511 MR298692
92 W P Thurston, On the structure of the group of volume preserving diffeomorphisms, preprint (1973)
93 W P Thurston, Hyperbolic structures on 3-manifolds, II : Surface groups and 3-manifolds which fiber over the circle, preprint (1986) arXiv:math/9801045
94 B Tshishiku, Borel’s stable range for the cohomology of arithmetic groups, J. Lie Theory 29 (2019) 1093 MR4022145
95 T Tsuboi, On the uniform perfectness of diffeomorphism groups, from: "Groups of diffeomorphisms", Adv. Stud. Pure Math. 52, Math. Soc. Japan (2008) 505 MR2509724
96 T Tsuboi, On the uniform perfectness of the groups of diffeomorphisms of even-dimensional manifolds, Comment. Math. Helv. 87 (2012) 141 MR2874899
97 T Tsuboi, Several problems on groups of diffeomorphisms, from: "Geometry, dynamics, and foliations", Adv. Stud. Pure Math. 72, Math. Soc. Japan (2017) 239 MR3726712