Algebraic & Geometric Topology Volume 21, issue 4 (2021)

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The compression body graph has infinite diameter

Joseph Maher and Saul Schleimer

Algebraic & Geometric Topology 21 (2021) 1817–1856

DOI: 10.2140/agt.2021.21.1817

Bibliography

1	R Ackermann, An alternative approach to extending pseudo-Anosovs over compression bodies, Algebr. Geom. Topol. 15 (2015) 2383 MR3402343
2	I Agol, M H Freedman, Embedding Heegaard decompositions, preprint (2019) arXiv:1906.03244
3	I Biringer, J Johnson, Y Minsky, Extending pseudo-Anosov maps into compression bodies, J. Topol. 6 (2013) 1019 MR3145149
4	I Biringer, N G Vlamis, Automorphisms of the compression body graph, J. Lond. Math. Soc. 95 (2017) 94 MR3653085
5	B H Bowditch, Relatively hyperbolic groups, Int. J. Algebra Comput. 22 (2012) MR2922380
6	S D Burton, J S Purcell, Geodesic systems of tunnels in hyperbolic 3–manifolds, Algebr. Geom. Topol. 14 (2014) 925 MR3160607
7	A J Casson, D D Long, Algorithmic compression of surface automorphisms, Invent. Math. 81 (1985) 295 MR799268
8	M Coornaert, T Delzant, A Papadopoulos, Géométrie et théorie des groupes, 1441, Springer (1990) MR1075994
9	V Dang, J S Purcell, Cusp shape and tunnel number, Proc. Amer. Math. Soc. 147 (2019) 1351 MR3896079
10	S Dowdall, S J Taylor, The co-surface graph and the geometry of hyperbolic free group extensions, J. Topol. 10 (2017) 447 MR3653318
11	N M Dunfield, W P Thurston, Finite covers of random 3–manifolds, Invent. Math. 166 (2006) 457 MR2257389
12	U Hamenstädt, Train tracks and the Gromov boundary of the complex of curves, from: "Spaces of Kleinian groups" (editors Y N Minsky, M Sakuma, C Series), Lond. Math. Soc. Lect. Note Ser. 329, Cambridge Univ. Press (2006) 187 MR2258749
13	J Hempel, 3–manifolds as viewed from the curve complex, Topology 40 (2001) 631 MR1838999
14	V A Kaimanovich, H Masur, The Poisson boundary of the mapping class group, Invent. Math. 125 (1996) 221 MR1395719
15	I Kapovich, K Rafi, On hyperbolicity of free splitting and free factor complexes, Groups Geom. Dyn. 8 (2014) 391 MR3231221
16	E Klarreich, The boundary at infinity of the curve complex and the relative Teichmüller space, preprint (2008) arXiv:1803.10339
17	T Kobayashi, Heights of simple loops and pseudo-Anosov homeomorphisms, from: "Braids" (editors J S Birman, A Libgober), Contemp. Math. 78, Amer. Math. Soc. (1988) 327 MR975087
18	A Lubotzky, J Maher, C Wu, Random methods in 3–manifold theory, Tr. Mat. Inst. Steklova 292 (2016) 124 MR3628457
19	M Lustig, Y Moriah, Are large distance Heegaard splittings generic ?, J. Reine Angew. Math. 670 (2012) 93 MR2982693
20	J Ma, J Wang, Quasi-homomorphisms on mapping class groups vanishing on a handlebody group, preprint (2019) arXiv:1907.03290
21	J Maher, Random Heegaard splittings, J. Topol. 3 (2010) 997 MR2746344
22	J Maher, G Tiozzo, Random walks on weakly hyperbolic groups, J. Reine Angew. Math. 742 (2018) 187 MR3849626
23	H Masur, Measured foliations and handlebodies, Ergodic Theory Dynam. Systems 6 (1986) 99 MR837978
24	H A Masur, Y N Minsky, Geometry of the complex of curves, I : Hyperbolicity, Invent. Math. 138 (1999) 103 MR1714338
25	H A Masur, Y N Minsky, Geometry of the complex of curves, II : Hierarchical structure, Geom. Funct. Anal. 10 (2000) 902 MR1791145
26	H A Masur, Y N Minsky, Quasiconvexity in the curve complex, from: "In the tradition of Ahlfors and Bers, III" (editors W Abikoff, A Haas), Contemp. Math. 355, Amer. Math. Soc. (2004) 309 MR2145071
27	H Masur, L Mosher, S Schleimer, On train-track splitting sequences, Duke Math. J. 161 (2012) 1613 MR2942790
28	J Morgan, G Tian, Ricci flow and the Poincaré conjecture, 3, Amer. Math. Soc. (2007) MR2334563
29	R C Penner, J L Harer, Combinatorics of train tracks, 125, Princeton Univ. Press (1992) MR1144770
30	I Rivin, Walks on groups, counting reducible matrices, polynomials, and surface and free group automorphisms, Duke Math. J. 142 (2008) 353 MR2401624
31	M Scharlemann, M Tomova, Alternate Heegaard genus bounds distance, Geom. Topol. 10 (2006) 593 MR2224466
32	W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417 MR956596