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

Volume 25
Issue 7, 3789–4436
Issue 6, 3145–3787
Issue 5, 2527–3144
Issue 4, 1917–2526
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

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
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(), 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