Geometry & Topology Volume 28, issue 4 (2024)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Sublinearly Morse boundary, II: Proper geodesic spaces

Yulan Qing, Kasra Rafi and Giulio Tiozzo

Geometry & Topology 28 (2024) 1829–1889

DOI: 10.2140/gt.2024.28.1829

Bibliography

1	Y Algom-Kfir, Strongly contracting geodesics in outer space, Geom. Topol. 15 (2011) 2181 MR2862155
2	G N Arzhantseva, C H Cashen, J Tao, Growth tight actions, Pacific J. Math. 278 (2015) 1 MR3404665
3	G N Arzhantseva, C H Cashen, D Gruber, D Hume, Characterizations of Morse quasi-geodesics via superlinear divergence and sublinear contraction, Doc. Math. 22 (2017) 1193 MR3690269
4	J A Behrstock, Asymptotic geometry of the mapping class group and Teichmüller space, Geom. Topol. 10 (2006) 1523 MR2255505
5	J Behrstock, M F Hagen, A Sisto, Hierarchically hyperbolic spaces, I : Curve complexes for cubical groups, Geom. Topol. 21 (2017) 1731 MR3650081
6	M Bestvina, K Fujiwara, A characterization of higher rank symmetric spaces via bounded cohomology, Geom. Funct. Anal. 19 (2009) 11 MR2507218
7	S Blachère, P Haïssinsky, P Mathieu, Asymptotic entropy and Green speed for random walks on countable groups, Ann. Probab. 36 (2008) 1134 MR2408585
8	N Bourbaki, General topology, chapters 1–4, Springer (1989) MR979294
9	D Calegari, J Maher, Statistics and compression of scl, Ergodic Theory Dynam. Systems 35 (2015) 64 MR3294292
10	C H Cashen, J M Mackay, A metrizable topology on the contracting boundary of a group, Trans. Amer. Math. Soc. 372 (2019) 1555 MR3976570
11	R Charney, H Sultan, Contracting boundaries of CAT(0) spaces, J. Topol. 8 (2015) 93 MR3339446
12	G Choquet, J Deny, Sur l’équation de convolution μ = μ ∗ σ, C. R. Acad. Sci. Paris 250 (1960) 799 MR0119041
13	M Cordes, Morse boundaries of proper geodesic metric spaces, Groups Geom. Dyn. 11 (2017) 1281 MR3737283
14	M Cordes, M Dussaule, I Gekhtman, An embedding of the Morse boundary in the Martin boundary, Algebr. Geom. Topol. 22 (2022) 1217 MR4474783
15	C B Croke, B Kleiner, Spaces with nonpositive curvature and their ideal boundaries, Topology 39 (2000) 549 MR1746908
16	C Druţu, Quasi-isometric classification of non-uniform lattices in semisimple groups of higher rank, Geom. Funct. Anal. 10 (2000) 327 MR1771426
17	M Duchin, K Rafi, Divergence of geodesics in Teichmüller space and the mapping class group, Geom. Funct. Anal. 19 (2009) 722 MR2563768
18	E B Dynkin, M B Maljutov, Random walk on groups with a finite number of generators, Dokl. Akad. Nauk SSSR 137 (1961) 1042 MR0131904
19	A Eskin, D Fisher, K Whyte, Coarse differentiation of quasi-isometries, I : Spaces not quasi-isometric to Cayley graphs, Ann. of Math. 176 (2012) 221 MR2925383
20	A Eskin, D Fisher, K Whyte, Coarse differentiation of quasi-isometries, II : Rigidity for Sol and lamplighter groups, Ann. of Math. 177 (2013) 869 MR3034290
21	A Eskin, H Masur, K Rafi, Large-scale rank of Teichmüller space, Duke Math. J. 166 (2017) 1517 MR3659941
22	A Eskin, H Masur, K Rafi, Rigidity of Teichmüller space, Geom. Topol. 22 (2018) 4259 MR3890777
23	B Farb, H Masur, Superrigidity and mapping class groups, Topology 37 (1998) 1169 MR1632912
24	W J Floyd, Group completions and limit sets of Kleinian groups, Invent. Math. 57 (1980) 205 MR0568933
25	B Forghani, G Tiozzo, Shannon’s theorem for locally compact groups, Ann. Probab. 50 (2022) 61 MR4385123
26	A H Frink, Distance functions and the metrization problem, Bull. Amer. Math. Soc. 43 (1937) 133 MR1563501
27	H Furstenberg, A Poisson formula for semi-simple Lie groups, Ann. of Math. 77 (1963) 335 MR0146298
28	I Gekhtman, Y Qing, K Rafi, Genericity of sublinearly morse directions in CAT(0) spaces and the Teichmüller space, preprint (2022) arXiv:2208.04778
29	M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR0919829
30	V A Kaimanovich, The Poisson boundary of hyperbolic groups, C. R. Acad. Sci. Paris Sér. I Math. 318 (1994) 59 MR1260536
31	V A Kaimanovich, Boundaries of invariant Markov operators : the identification problem, from: "Ergodic theory of ℤ^d actions" (editors M Pollicott, K Schmidt), Lond. Math. Soc. Lect. Note Ser. 228, Cambridge Univ. Press (1996) 127 MR1411218
32	V A Kaimanovich, The Poisson formula for groups with hyperbolic properties, Ann. of Math. 152 (2000) 659 MR1815698
33	V A Kaimanovich, H Masur, The Poisson boundary of the mapping class group, Invent. Math. 125 (1996) 221 MR1395719
34	V A Kaimanovich, H Masur, The Poisson boundary of Teichmüller space, J. Funct. Anal. 156 (1998) 301 MR1636940
35	A Kar, Asymptotically CAT(0) groups, Publ. Mat. 55 (2011) 67 MR2779576
36	A Karlsson, G A Margulis, A multiplicative ergodic theorem and nonpositively curved spaces, Comm. Math. Phys. 208 (1999) 107 MR1729880
37	A Karlsson, G A Noskov, Some groups having only elementary actions on metric spaces with hyperbolic boundaries, Geom. Dedicata 104 (2004) 119 MR2043957
38	E Klarreich, The boundary at infinity of the curve complex and the relative Teichmüller space, Groups Geom. Dyn. 16 (2022) 705 MR4502619
39	J Maher, Linear progress in the complex of curves, Trans. Amer. Math. Soc. 362 (2010) 2963 MR2592943
40	J Maher, Exponential decay in the mapping class group, J. Lond. Math. Soc. 86 (2012) 366 MR2980916
41	J Maher, G Tiozzo, Random walks on weakly hyperbolic groups, J. Reine Angew. Math. 742 (2018) 187 MR3849626
42	H A Masur, Y N Minsky, Geometry of the complex of curves, II : Hierarchical structure, Geom. Funct. Anal. 10 (2000) 902 MR1791145
43	P Mathieu, A Sisto, Deviation inequalities for random walks, Duke Math. J. 169 (2020) 961 MR4079419
44	H M Morse, A fundamental class of geodesics on any closed surface of genus greater than one, Trans. Amer. Math. Soc. 26 (1924) 25 MR1501263
45	H T Nguyen, Y Qing, Sublinearly Morse boundary of CAT(0) admissible groups, J. Group Theory (2024)
46	A Y Olshanskii, D V Osin, M V Sapir, Lacunary hyperbolic groups, Geom. Topol. 13 (2009) 2051 MR2507115
47	Y Qing, K Rafi, Sublinearly Morse boundary, I : CAT(0) spaces, Adv. Math. 404 (2022) 108442 MR4423805
48	Y Qing, G Tiozzo, Excursions of generic geodesics in right-angled Artin groups and graph products, Int. Math. Res. Not. 2021 (2021) 16910 MR4345818
49	K Rafi, Y Verberne, Geodesics in the mapping class group, Algebr. Geom. Topol. 21 (2021) 2995 MR4344876
50	C Series, Martin boundaries of random walks on Fuchsian groups, Israel J. Math. 44 (1983) 221 MR0693661
51	A Sisto, On metric relative hyperbolicity, preprint (2012) arXiv:1210.8081
52	A Sisto, Projections and relative hyperbolicity, Enseign. Math. 59 (2013) 165 MR3113603
53	A Sisto, Tracking rates of random walks, Israel J. Math. 220 (2017) 1 MR3666817
54	A Sisto, Contracting elements and random walks, J. Reine Angew. Math. 742 (2018) 79 MR3849623
55	A Sisto, S J Taylor, Largest projections for random walks and shortest curves in random mapping tori, Math. Res. Lett. 26 (2019) 293 MR3963985
56	G Tiozzo, Sublinear deviation between geodesics and sample paths, Duke Math. J. 164 (2015) 511 MR3314479
57	W y Yang, Genericity of contracting elements in groups, Math. Ann. 376 (2020) 823 MR4081104