Algebraic & Geometric Topology Volume 25, issue 9 (2025)

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ISSN (electronic): 1472-2739

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Characterizations of stability via Morse limit sets

Jacob Garcia

Algebraic & Geometric Topology 25 (2025) 5541–5566

DOI: 10.2140/agt.2025.25.5541

Bibliography

1	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
2	Y Antolín, M Mj, A Sisto, S J Taylor, Intersection properties of stable subgroups and bounded cohomology, Indiana Univ. Math. J. 68 (2019) 179 MR3922043
3	T Aougab, M G Durham, S J Taylor, Pulling back stability with applications to Out(F_n) and relatively hyperbolic groups, J. Lond. Math. Soc. 96 (2017) 565 MR3742433
4	S Balasubramanya, M Chesser, A Kerr, J Mangahas, M Trin, (Non-)recognizing spaces for stable subgroups, Proc. Amer. Math. Soc. 153 (2025) 3197 MR4923441
5	J A Behrstock, Asymptotic geometry of the mapping class group and Teichmüller space, Geom. Topol. 10 (2006) 1523 MR2255505
6	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
7	M Clay, D Margalit, editors, Office hours with a geometric group theorist, Princeton Univ. Press (2017) MR3587214
8	M Cordes, Morse boundaries of proper geodesic metric spaces, Groups Geom. Dyn. 11 (2017) 1281 MR3737283
9	M Cordes, M G Durham, Boundary convex cocompactness and stability of subgroups of finitely generated groups, Int. Math. Res. Not. 2019 (2019) 1699 MR3932592
10	M Cordes, D Hume, Stability and the Morse boundary, J. Lond. Math. Soc. 95 (2017) 963 MR3664526
11	M Cordes, J Russell, D Spriano, A Zalloum, Regularity of Morse geodesics and growth of stable subgroups, J. Topol. 15 (2022) 1217 MR4461848
12	S Dowdall, S J Taylor, Hyperbolic extensions of free groups, Geom. Topol. 22 (2018) 517 MR3720349
13	M G Durham, S J Taylor, Convex cocompactness and stability in mapping class groups, Algebr. Geom. Topol. 15 (2015) 2839 MR3426695
14	B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
15	B Farb, L Mosher, Convex cocompact subgroups of mapping class groups, Geom. Topol. 6 (2002) 91 MR1914566
16	A Fathi, F Laudenbach, V Poénaru, Thurston’s work on surfaces, 48, Princeton Univ. Press (2012) MR3053012
17	U Hamenstädt, Word hyperbolic extensions of surface groups, preprint (2005) arXiv:math/0505244
18	U Hamenstädt, S Hensel, Stability in outer space, Groups Geom. Dyn. 12 (2018) 359 MR3781424
19	I Kapovich, N Benakli, Boundaries of hyperbolic groups, from: "Combinatorial and geometric group theory", Contemp. Math. 296, Amer. Math. Soc. (2002) 39 MR1921706
20	R P Kent IV, C J Leininger, Shadows of mapping class groups : capturing convex cocompactness, Geom. Funct. Anal. 18 (2008) 1270 MR2465691
21	H Kim, Stable subgroups and Morse subgroups in mapping class groups, Internat. J. Algebra Comput. 29 (2019) 893 MR3978121
22	Q Liu, Dynamics on the Morse boundary, Geom. Dedicata 214 (2021) 1 MR4308266
23	A Marden, The geometry of finitely generated kleinian groups, Ann. of Math. 99 (1974) 383 MR349992
24	H A Masur, Y N Minsky, Geometry of the complex of curves, II : Hierarchical structure, Geom. Funct. Anal. 10 (2000) 902 MR1791145
25	J Russell, D Spriano, H C Tran, The local-to-global property for Morse quasi-geodesics, Math. Z. 300 (2022) 1557 MR4363788
26	J Russell, D Spriano, H C Tran, Convexity in hierarchically hyperbolic spaces, Algebr. Geom. Topol. 23 (2023) 1167 MR4598806
27	D Sullivan, Quasiconformal homeomorphisms and dynamics, I : Solution of the Fatou–Julia problem on wandering domains, Ann. of Math. 122 (1985) 401 MR819553
28	E L Swenson, Quasi-convex groups of isometries of negatively curved spaces, Topology Appl. 110 (2001) 119 MR1804703
29	H C Tran, On strongly quasiconvex subgroups, Geom. Topol. 23 (2019) 1173 MR3956891
30	S Zbinden, Hyperbolic spaces that detect all strongly-contracting directions, preprint (2024) arXiv:2404.12162