An embedding of the Morse boundary in the Martin boundary

Matthew Cordes; Matthieu Dussaule; Ilya Gekhtman

doi:10.2140/agt.2022.22.1217

An embedding of the Morse boundary in the Martin boundary

Matthew Cordes, Matthieu Dussaule, Ilya Gekhtman

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We construct a one-to-one continuous map from the Morse boundary of a hierarchically hyperbolic group to its Martin boundary. This construction is based on deviation inequalities generalizing Ancona’s work on hyperbolic groups. This provides a possibly new metrizable topology on the Morse boundary of such groups. We also prove that the Morse boundary has measure 0 with respect to the harmonic measure unless the group is hyperbolic.

Original language	English
Pages (from-to)	1217-1253
Number of pages	37
Journal	Algebraic and Geometric Topology
Volume	22
Issue number	3
DOIs	https://doi.org/10.2140/agt.2022.22.1217
State	Published - 2022

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.2140/agt.2022.22.1217

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title = "An embedding of the Morse boundary in the Martin boundary",

abstract = "We construct a one-to-one continuous map from the Morse boundary of a hierarchically hyperbolic group to its Martin boundary. This construction is based on deviation inequalities generalizing Ancona{\textquoteright}s work on hyperbolic groups. This provides a possibly new metrizable topology on the Morse boundary of such groups. We also prove that the Morse boundary has measure 0 with respect to the harmonic measure unless the group is hyperbolic.",

author = "Matthew Cordes and Matthieu Dussaule and Ilya Gekhtman",

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doi = "10.2140/agt.2022.22.1217",

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AU - Cordes, Matthew

AU - Dussaule, Matthieu

AU - Gekhtman, Ilya

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N2 - We construct a one-to-one continuous map from the Morse boundary of a hierarchically hyperbolic group to its Martin boundary. This construction is based on deviation inequalities generalizing Ancona’s work on hyperbolic groups. This provides a possibly new metrizable topology on the Morse boundary of such groups. We also prove that the Morse boundary has measure 0 with respect to the harmonic measure unless the group is hyperbolic.

AB - We construct a one-to-one continuous map from the Morse boundary of a hierarchically hyperbolic group to its Martin boundary. This construction is based on deviation inequalities generalizing Ancona’s work on hyperbolic groups. This provides a possibly new metrizable topology on the Morse boundary of such groups. We also prove that the Morse boundary has measure 0 with respect to the harmonic measure unless the group is hyperbolic.

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U2 - 10.2140/agt.2022.22.1217

DO - 10.2140/agt.2022.22.1217

M3 - مقالة

SN - 1472-2747

VL - 22

SP - 1217

EP - 1253

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 3

ER -

An embedding of the Morse boundary in the Martin boundary

Abstract

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