Algebraic & Geometric Topology Volume 25, issue 5 (2025)

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

Product set growth in virtual subgroups of mapping class groups

Alice Kerr

Algebraic & Geometric Topology 25 (2025) 2757–2806

DOI: 10.2140/agt.2025.25.2757

Bibliography

1	Y Antolín, A Minasyan, Tits alternatives for graph products, J. Reine Angew. Math. 704 (2015) 55 MR3365774
2	T Aougab, Uniform hyperbolicity of the graphs of curves, Geom. Topol. 17 (2013) 2855 MR3190300
3	S H Balasubramanya, Acylindrical group actions on quasi-trees, Algebr. Geom. Topol. 17 (2017) 2145 MR3685605
4	G Baumslag, A Myasnikov, V Remeslennikov, Algebraic geometry over groups, I : Algebraic sets and ideal theory, J. Algebra 219 (1999) 16 MR1707663
5	J S Birman, A Lubotzky, J McCarthy, Abelian and solvable subgroups of the mapping class group, Duke Math. J. 50 (1983) 1107 MR726319
6	B H Bowditch, Tight geodesics in the curve complex, Invent. Math. 171 (2008) 281 MR2367021
7	E Breuillard, K Fujiwara, On the joint spectral radius for isometries of non-positively curved spaces and uniform growth, Ann. Inst. Fourier (Grenoble) 71 (2021) 317 MR4275871
8	J O Button, Explicit Helfgott type growth in free products and in limit groups, J. Algebra 389 (2013) 61 MR3065992
9	R Charney, K Vogtmann, Finiteness properties of automorphism groups of right-angled Artin groups, Bull. Lond. Math. Soc. 41 (2009) 94 MR2481994
10	M T Clay, C J Leininger, J Mangahas, The geometry of right-angled Artin subgroups of mapping class groups, Groups Geom. Dyn. 6 (2012) 249 MR2914860
11	M Clay, K Rafi, S Schleimer, Uniform hyperbolicity of the curve graph via surgery sequences, Algebr. Geom. Topol. 14 (2014) 3325 MR3302964
12	M Coornaert, T Delzant, A Papadopoulos, Géométrie et théorie des groupes : les groupes hyperboliques de Gromov, 1441, Springer (1990) MR1075994
13	R Coulon, M Steenbock, Product set growth in Burnside groups, J. Éc. polytech. Math. 9 (2022) 463 MR4387462
14	Y M Cui, Y P Jiang, W Y Yang, Lower bound on growth of non-elementary subgroups in relatively hyperbolic groups, J. Group Theory 25 (2022) 799 MR4472896
15	F Dahmani, V Guirardel, D Osin, Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces, 1156, Amer. Math. Soc. (2017) MR3589159
16	T Delzant, M Steenbock, Product set growth in groups and hyperbolic geometry, J. Topol. 13 (2020) 1183 MR4100130
17	A J Duncan, I V Kazachkov, V N Remeslennikov, Parabolic and quasiparabolic subgroups of free partially commutative groups, J. Algebra 318 (2007) 918 MR2371978
18	A Eskin, S Mozes, H Oh, On uniform exponential growth for linear groups, Invent. Math. 160 (2005) 1 MR2129706
19	B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
20	K Fujiwara, The rates of growth in an acylindrically hyperbolic group, Groups Geom. Dynam. 19 (2025) 109
21	K Fujiwara, Z Sela, The rates of growth in a hyperbolic group, Invent. Math. 233 (2023) 1427 MR4623546
22	M Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981) 53 MR623534
23	M Gromov, Hyperbolic groups, from: "Essays in group theory", Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
24	F Haglund, D T Wise, Special cube complexes, Geom. Funct. Anal. 17 (2008) 1551 MR2377497
25	F Haglund, D T Wise, Coxeter groups are virtually special, Adv. Math. 224 (2010) 1890 MR2646113
26	H A Helfgott, Growth and generation in SL₂(ℤ∕pℤ), Ann. of Math. 167 (2008) 601 MR2415382
27	S Hensel, P Przytycki, R C H Webb, 1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs, J. Eur. Math. Soc. 17 (2015) 755 MR3336835
28	T Hsu, D T Wise, On linear and residual properties of graph products, Michigan Math. J. 46 (1999) 251 MR1704150
29	N V Ivanov, Algebraic properties of the Teichmüller modular group, Dokl. Akad. Nauk SSSR 275 (1984) 786 MR745513
30	N V Ivanov, Subgroups of Teichmüller modular groups, 115, Amer. Math. Soc. (1992) MR1195787
31	I Kapovich, D T Wise, The equivalence of some residual properties of word-hyperbolic groups, J. Algebra 223 (2000) 562 MR1735163
32	A Kerr, Quasi-trees and product set growth, PhD thesis, University of Oxford (2022)
33	A Kerr, Tree approximation in quasi-trees, Groups Geom. Dyn. 17 (2023) 1193 MR4641367
34	S H Kim, T Koberda, Embedability between right-angled Artin groups, Geom. Topol. 17 (2013) 493 MR3039768
35	S H Kim, T Koberda, The geometry of the curve graph of a right-angled Artin group, Internat. J. Algebra Comput. 24 (2014) 121 MR3192368
36	S H Kim, T Koberda, An obstruction to embedding right-angled Artin groups in mapping class groups, Int. Math. Res. Not. 2014 (2014) 3912 MR3239092
37	T Koberda, Right-angled Artin groups and a generalized isomorphism problem for finitely generated subgroups of mapping class groups, Geom. Funct. Anal. 22 (2012) 1541 MR3000498
38	J Mangahas, Uniform uniform exponential growth of subgroups of the mapping class group, Geom. Funct. Anal. 19 (2010) 1468 MR2585580
39	J Mangahas, A recipe for short-word pseudo-Anosovs, Amer. J. Math. 135 (2013) 1087 MR3086070
40	A Mann, How groups grow, 395, Cambridge Univ. Press (2012) MR2894945
41	J F Manning, Geometry of pseudocharacters, Geom. Topol. 9 (2005) 1147 MR2174263
42	H A Masur, Y N Minsky, Geometry of the complex of curves, I : Hyperbolicity, Invent. Math. 138 (1999) 103 MR1714338
43	J McCarthy, A “Tits-alternative” for subgroups of surface mapping class groups, Trans. Amer. Math. Soc. 291 (1985) 583 MR800253
44	D V Osin, Algebraic entropy of elementary amenable groups, Geom. Dedicata 107 (2004) 133 MR2110759
45	D Osin, Acylindrically hyperbolic groups, Trans. Amer. Math. Soc. 368 (2016) 851 MR3430352
46	S R Safin, Powers of subsets of free groups, Mat. Sb. 202 (2011) 97 MR2907200
47	J P Serre, Trees, Springer (1980) MR607504
48	P B Shalen, P Wagreich, Growth rates, Z_p-homology, and volumes of hyperbolic 3-manifolds, Trans. Amer. Math. Soc. 331 (1992) 895 MR1156298
49	J Stallings, Groups of dimension 1 are locally free, Bull. Amer. Math. Soc. 74 (1968) 361 MR223439
50	T Tao, Product set estimates for non-commutative groups, Combinatorica 28 (2008) 547 MR2501249
51	R Wan, W Yang, Uniform exponential growth for groups with proper product actions on hyperbolic spaces, preprint (2023) arXiv:2307.08400
52	J S Wilson, On exponential growth and uniformly exponential growth for groups, Invent. Math. 155 (2004) 287 MR2031429
53	X Xie, Growth of relatively hyperbolic groups, Proc. Amer. Math. Soc. 135 (2007) 695 MR2262865