Algebraic & Geometric Topology Volume 26, issue 3 (2026)

Download this article
	For screen
	For printing

Recent 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

Relative bounded cohomology on groups with contracting elements

Zhenguo Huangfu and Renxing Wan

Algebraic & Geometric Topology 26 (2026) 1195–1227

DOI: 10.2140/agt.2026.26.1195

Bibliography

1	G N Arzhantseva, C H Cashen, D Gruber, D Hume, Negative curvature in graphical small cancellation groups, Groups Geom. Dyn. 13 (2019) 579 MR3950644
2	W Ballmann, Lectures on spaces of nonpositive curvature, 25, Birkhäuser (1995) MR1377265
3	M Bestvina, K Bromberg, K Fujiwara, Constructing group actions on quasi-trees and applications to mapping class groups, Publ. Math. Inst. Hautes Études Sci. 122 (2015) 1 MR3415065
4	M Bestvina, K Bromberg, K Fujiwara, A Sisto, Acylindrical actions on projection complexes, Enseign. Math. 65 (2019) 1 MR4057354
5	M Bestvina, K Fujiwara, Bounded cohomology of subgroups of mapping class groups, Geom. Topol. 6 (2002) 69 MR1914565
6	M Bestvina, K Fujiwara, A characterization of higher rank symmetric spaces via bounded cohomology, Geom. Funct. Anal. 19 (2009) 11 MR2507218
7	A Bouarich, Suites exactes en cohomologie bornée réelle des groupes discrets, C. R. Acad. Sci. Paris Sér. I Math. 320 (1995) 1355 MR1338286
8	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
9	R Brooks, Some remarks on bounded cohomology, from: "Riemann surfaces and related topics" (editors I Kra, B Maskit), Ann. of Math. Stud. 97, Princeton Univ. Press (1981) 53 MR624804
10	K S Brown, Cohomology of groups, 87, Springer (1994) MR1324339
11	M Bucher, M Burger, R Frigerio, A Iozzi, C Pagliantini, M B Pozzetti, Isometric embeddings in bounded cohomology, J. Topol. Anal. 6 (2014) 1 MR3190136
12	D Calegari, scl, 20, Mathematical Society of Japan (2009) MR2527432
13	M Coornaert, T Delzant, A Papadopoulos, Géométrie et théorie des groupes : les groupes hyperboliques de Gromov, 1441, Springer (1990) MR1075994
14	F Dahmani, V Guirardel, D Osin, Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces, 1156, Amer. Math. Soc. (2017) MR3589159
15	T Delzant, Sous-groupes distingués et quotients des groupes hyperboliques, Duke Math. J. 83 (1996) 661 MR1390660
16	C Druţu, M Kapovich, Geometric group theory, 63, Amer. Math. Soc. (2018) MR3753580
17	C Druţu, M Sapir, Tree-graded spaces and asymptotic cones of groups, Topology 44 (2005) 959 MR2153979
18	D B A Epstein, K Fujiwara, The second bounded cohomology of word-hyperbolic groups, Topology 36 (1997) 1275 MR1452851
19	B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
20	A Fathi, F Laudenbach, V Poenaru, Travaux de Thurston sur les surfaces : Séminaire Orsay, 66-67, Soc. Math. France (1979) 284 MR568308
21	F Franceschini, A characterization of relatively hyperbolic groups via bounded cohomology, Groups Geom. Dyn. 12 (2018) 919 MR3845713
22	R Frigerio, Bounded cohomology of discrete groups, 227, Amer. Math. Soc. (2017) MR3726870
23	R Frigerio, M B Pozzetti, A Sisto, Extending higher-dimensional quasi-cocycles, J. Topol. 8 (2015) 1123 MR3431671
24	K Fujiwara, The second bounded cohomology of a group acting on a Gromov-hyperbolic space, Proc. London Math. Soc. (3) 76 (1998) 70 MR1476898
25	K Fujiwara, The second bounded cohomology of an amalgamated free product of groups, Trans. Amer. Math. Soc. 352 (2000) 1113 MR1491864
26	V Gerasimov, L Potyagailo, Quasiconvexity in relatively hyperbolic groups, J. Reine Angew. Math. 710 (2016) 95 MR3437561
27	É Ghys, P de la Harpe, editors, Sur les groupes hyperboliques d’après Mikhael Gromov, 83, Birkhäuser (1990) MR1086648
28	M Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. 56 (1982) 5 MR686042
29	M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
30	U Hamenstädt, Bounded cohomology and isometry groups of hyperbolic spaces, J. Eur. Math. Soc. 10 (2008) 315 MR2390326
31	S Han, W Yang, Y Zou, Counting double cosets with application to generic 3-manifolds, preprint (2023) arXiv:2307.06169
32	Z He, J Liu, W Yang, Large quotients of group actions with a contracting element, from: "Proceedings of the International Consortium of Chinese Mathematicians 2017" (editors S Y Cheng, S T Yau, L Ji, X P Zhu), Int. Press (2020) 319 MR4251117
33	M Hull, D Osin, Induced quasicocycles on groups with hyperbolically embedded subgroups, Algebr. Geom. Topol. 13 (2013) 2635 MR3116299
34	N V Ivanov, Foundations of the theory of bounded cohomology, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 143 (1985) 69 MR806562
35	S Kim, T Kuessner, Simplicial volume of compact manifolds with amenable boundary, J. Topol. Anal. 7 (2015) 23 MR3284388
36	D Kotschick, Quasi-homomorphisms and stable lengths in mapping class groups, Proc. Amer. Math. Soc. 132 (2004) 3167 MR2073290
37	Y N Minsky, Quasi-projections in Teichmüller space, J. Reine Angew. Math. 473 (1996) 121 MR1390685
38	N Monod, Continuous bounded cohomology of locally compact groups, 1758, Springer (2001) MR1840942
39	B H Neumann, Groups covered by permutable subsets, J. London Math. Soc. 29 (1954) 236 MR62122
40	D V Osin, Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems, 843, Amer. Math. Soc. (2006) MR2182268
41	D Osin, Acylindrically hyperbolic groups, Trans. Amer. Math. Soc. 368 (2016) 851 MR3430352
42	C Pagliantini, P Rolli, Relative second bounded cohomology of free groups, Geom. Dedicata 175 (2015) 267 MR3323641
43	H Park, Relative bounded cohomology, Topology Appl. 131 (2003) 203 MR1983079
44	P Przytycki, A Sisto, A note on acylindrical hyperbolicity of mapping class groups, from: "Hyperbolic geometry and geometric group theory" (editors K Fujiwara, S Kojima, K Ohshika), Adv. Stud. Pure Math. 73, Math. Soc. Japan (2017) 255 MR3728501
45	A Sisto, Contracting elements and random walks, J. Reine Angew. Math. 742 (2018) 79 MR3849623
46	R Wan, X Xu, W Yang, Marked length spectrum rigidity in groups with contracting elements, preprint (2024) arXiv:2402.10165
47	W y Yang, Growth tightness for groups with contracting elements, Math. Proc. Cambridge Philos. Soc. 157 (2014) 297 MR3254594
48	W y Yang, Statistically convex-cocompact actions of groups with contracting elements, Int. Math. Res. Not. 2019 (2019) 7259 MR4039013
49	W Yang, Conformal dynamics at infinity for groups with contracting elements, preprint (2022) arXiv:2208.04861