TY - UNPB
T1 - Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity
AU - Goldsborough, Antoine
AU - Hagen, Mark
AU - Petyt, Harry
AU - Russell, Jacob
AU - Sisto, Alessandro
N1 - 36 pages, 1 figure. Main paper by A. Goldsborough, M. Hagen, H. Petyt and A. Sisto; appendix by J. Russell
PY - 2023/9/13
Y1 - 2023/9/13
N2 - We show that quasi-isometries of (well-behaved) hierarchically hyperbolic groups descend to quasi-isometries of their maximal hyperbolic space. This has two applications, one relating to quasi-isometry invariance of acylindrical hyperbolicity, and the other a linear progress result for Markov chains. The appendix, by Jacob Russell, contains a partial converse under the (necessary) condition that the maximal hyperbolic space is one-ended.
AB - We show that quasi-isometries of (well-behaved) hierarchically hyperbolic groups descend to quasi-isometries of their maximal hyperbolic space. This has two applications, one relating to quasi-isometry invariance of acylindrical hyperbolicity, and the other a linear progress result for Markov chains. The appendix, by Jacob Russell, contains a partial converse under the (necessary) condition that the maximal hyperbolic space is one-ended.
KW - math.GR
KW - math.PR
U2 - 10.48550/arXiv.2309.07013
DO - 10.48550/arXiv.2309.07013
M3 - Preprint
BT - Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity
ER -