On uniqueness of coarse median structures

Elia Fioravanti; Alessandro Sisto

On uniqueness of coarse median structures

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

Abstract

We show that any product of bushy hyperbolic spaces has a unique coarse median structure, and that having a unique coarse median structure is a property closed under relative hyperbolicity. As a consequence, in contrast with the case of mapping class groups, there are non-hyperbolic pants graphs that have unique coarse median structures.

Original language	English
Journal	Algebraic and Geometric Topology
Publication status	Accepted/In press - 19 Aug 2025

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title = "On uniqueness of coarse median structures",

abstract = "We show that any product of bushy hyperbolic spaces has a unique coarse median structure, and that having a unique coarse median structure is a property closed under relative hyperbolicity. As a consequence, in contrast with the case of mapping class groups, there are non-hyperbolic pants graphs that have unique coarse median structures.",

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AU - Sisto, Alessandro

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AB - We show that any product of bushy hyperbolic spaces has a unique coarse median structure, and that having a unique coarse median structure is a property closed under relative hyperbolicity. As a consequence, in contrast with the case of mapping class groups, there are non-hyperbolic pants graphs that have unique coarse median structures.

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JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

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On uniqueness of coarse median structures

Abstract

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