Algebraic & Geometric Topology Volume 22, issue 3 (2022)

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An embedding of the Morse boundary in the Martin boundary

Matthew Cordes, Matthieu Dussaule and Ilya Gekhtman

Algebraic & Geometric Topology 22 (2022) 1217–1253

DOI: 10.2140/agt.2022.22.1217

Bibliography

1	C R Abbott, Not all finitely generated groups have universal acylindrical actions, Proc. Amer. Math. Soc. 144 (2016) 4151 MR3531168
2	C Abbott, S H Balasubramanya, D Osin, Hyperbolic structures on groups, Algebr. Geom. Topol. 19 (2019) 1747 MR3995018
3	C Abbott, J Behrstock, M G Durham, Largest acylindrical actions and stability in hierarchically hyperbolic groups, Trans. Amer. Math. Soc. Ser. B 8 (2021) 66 MR4215647
4	A Ancona, Positive harmonic functions and hyperbolicity, from: "Potential theory: surveys and problems" (editors J Král, J Lukeš, I Netuka, J Veselý), Lecture Notes in Math. 1344, Springer (1988) 1 MR973878
5	A Ancona, Théorie du potentiel sur les graphes et les variétés, from: "École d’été de Probabilités de Saint–Flour, XVIII" (editor P L Hennequin), Lecture Notes in Math. 1427, Springer (1990) 1 MR1100282
6	J Behrstock, M F Hagen, A Sisto, Hierarchically hyperbolic spaces, I : Curve complexes for cubical groups, Geom. Topol. 21 (2017) 1731 MR3650081
7	J Behrstock, M Hagen, A Sisto, Hierarchically hyperbolic spaces II : Combination theorems and the distance formula, Pacific J. Math. 299 (2019) 257 MR3956144
8	S Blachère, S Brofferio, Internal diffusion limited aggregation on discrete groups having exponential growth, Probab. Theory Related Fields 137 (2007) 323 MR2278460
9	B H Bowditch, Tight geodesics in the curve complex, Invent. Math. 171 (2008) 281 MR2367021
10	B H Bowditch, Relatively hyperbolic groups, Internat. J. Algebra Comput. 22 (2012) MR2922380
11	C H Cashen, J M Mackay, A metrizable topology on the contracting boundary of a group, Trans. Amer. Math. Soc. 372 (2019) 1555 MR3976570
12	R Charney, M Cordes, D Murray, Quasi-Mobius homeomorphisms of Morse boundaries, Bull. Lond. Math. Soc. 51 (2019) 501 MR3964503
13	R Charney, H Sultan, Contracting boundaries of CAT(0) spaces, J. Topol. 8 (2015) 93 MR3339446
14	M Cordes, Morse boundaries of proper geodesic metric spaces, Groups Geom. Dyn. 11 (2017) 1281 MR3737283
15	M Cordes, A survey on Morse boundaries and stability, from: "Beyond hyperbolicity" (editors M Hagen, R Webb, H Wilton), London Math. Soc. Lecture Note Ser. 454, Cambridge Univ. Press (2019) 83 MR3966607
16	C Druţu, M Sapir, Tree-graded spaces and asymptotic cones of groups, Topology 44 (2005) 959 MR2153979
17	M Dussaule, I Gekhtman, V Gerasimov, L Potyagailo, The Martin boundary of relatively hyperbolic groups with virtually abelian parabolic subgroups, Enseign. Math. 66 (2020) 341 MR4254264
18	A Erschler, Boundary behavior for groups of subexponential growth, Ann. of Math. 160 (2004) 1183 MR2144977
19	A Erschler, Poisson–Furstenberg boundaries, large-scale geometry and growth of groups, from: "Proceedings of the International Congress of Mathematicians, II" (editors R Bhatia, A Pal, G Rangarajan, V Srinivas, M Vanninathan, P Gastesi), Hindustan (2010) 681 MR2827814
20	B Farb, Relatively hyperbolic groups, Geom. Funct. Anal. 8 (1998) 810 MR1650094
21	H Furstenberg, A Poisson formula for semi-simple Lie groups, Ann. of Math. 77 (1963) 335 MR146298
22	H Furstenberg, Boundary theory and stochastic processes on homogeneous spaces, from: "Harmonic analysis on homogeneous spaces" (editor C C Moore), Proc. Sympos. Pure Math. XXVI, Amer. Math. Soc. (1973) 193 MR0352328
23	I Gekhtman, V Gerasimov, L Potyagailo, W Yang, Martin boundary covers Floyd boundary, Invent. Math. 223 (2021) 759 MR4209863
24	S Gouëzel, Martin boundary of random walks with unbounded jumps in hyperbolic groups, Ann. Probab. 43 (2015) 2374 MR3395464
25	M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
26	M Incerti-Medici, Comparing topologies on the Morse boundary and quasi-isometry invariance, Geom. Dedicata 212 (2021) 153 MR4251668
27	V A Kaimanovich, Ergodicity of harmonic invariant measures for the geodesic flow on hyperbolic spaces, J. Reine Angew. Math. 455 (1994) 57 MR1293874
28	V A Kaimanovich, Boundaries of invariant Markov operators : the identification problem, from: "Ergodic theory of ℤ^d actions" (editors M Pollicott, K Schmidt), London Math. Soc. Lecture Note Ser. 228, Cambridge Univ. Press (1996) 127 MR1411218
29	V A Kaimanovich, The Poisson formula for groups with hyperbolic properties, Ann. of Math. 152 (2000) 659 MR1815698
30	V A Kaimanovich, H Masur, The Poisson boundary of the mapping class group, Invent. Math. 125 (1996) 221 MR1395719
31	V A Kaimanovich, A M Vershik, Random walks on discrete groups: boundary and entropy, Ann. Probab. 11 (1983) 457 MR704539
32	H Kesten, Full Banach mean values on countable groups, Math. Scand. 7 (1959) 146 MR112053
33	J Maher, G Tiozzo, Random walks on weakly hyperbolic groups, J. Reine Angew. Math. 742 (2018) 187 MR3849626
34	P Mathieu, A Sisto, Deviation inequalities for random walks, Duke Math. J. 169 (2020) 961 MR4079419
35	D Murray, Topology and dynamics of the contracting boundary of cocompact CAT(0) spaces, Pacific J. Math. 299 (2019) 89 MR3947271
36	D V Osin, Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems, 843, Amer. Math. Soc. (2006) MR2182268
37	D Osin, Acylindrically hyperbolic groups, Trans. Amer. Math. Soc. 368 (2016) 851 MR3430352
38	S A Sawyer, Martin boundaries and random walks, from: "Harmonic functions on trees and buildings" (editor A Korányi), Contemporary Math. 206, Amer. Math. Soc. (1997) 17 MR1463727
39	Z Sela, Acylindrical accessibility for groups, Invent. Math. 129 (1997) 527 MR1465334
40	A Sisto, Projections and relative hyperbolicity, Enseign. Math. 59 (2013) 165 MR3113603
41	A Sisto, What is a hierarchically hyperbolic space?, from: "Beyond hyperbolicity" (editors M Hagen, R Webb, H Wilton), London Math. Soc. Lecture Note Ser. 454, Cambridge Univ. Press (2019) 117 MR3966608
42	A Sisto, S J Taylor, Largest projections for random walks and shortest curves in random mapping tori, Math. Res. Lett. 26 (2019) 293 MR3963985
43	H C Tran, Divergence spectra and Morse boundaries of relatively hyperbolic groups, Geom. Dedicata 194 (2018) 99 MR3798063
44	W Woess, Random walks on infinite graphs and groups, 138, Cambridge Univ. Press (2000) MR1743100