Higson compactification and dimension raising

Kyle Austin; Žiga Virk

doi:10.1016/j.topol.2016.10.005

Higson compactification and dimension raising

Kyle Austin, Žiga Virk

Department of Mathematics

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

2 Scopus citations

Abstract

Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful in showing that the classical dimension raising theorems hold in large scale; that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely n-to-1 maps, which include the natural quotient maps via a finite group action, and prove that they preserve the asymptotic dimension.

Original language	English
Pages (from-to)	45-57
Number of pages	13
Journal	Topology and its Applications
Volume	215
DOIs	https://doi.org/10.1016/j.topol.2016.10.005
State	Published - 1 Jan 2017

Keywords

Asymptotic dimension
Higson compactification
Hurewicz theorems
N-to-1 maps

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2016.10.005

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title = "Higson compactification and dimension raising",

abstract = "Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful in showing that the classical dimension raising theorems hold in large scale; that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely n-to-1 maps, which include the natural quotient maps via a finite group action, and prove that they preserve the asymptotic dimension.",

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AU - Virk, Žiga

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N2 - Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful in showing that the classical dimension raising theorems hold in large scale; that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely n-to-1 maps, which include the natural quotient maps via a finite group action, and prove that they preserve the asymptotic dimension.

AB - Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful in showing that the classical dimension raising theorems hold in large scale; that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely n-to-1 maps, which include the natural quotient maps via a finite group action, and prove that they preserve the asymptotic dimension.

KW - Asymptotic dimension

KW - Higson compactification

KW - Hurewicz theorems

KW - N-to-1 maps

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DO - 10.1016/j.topol.2016.10.005

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VL - 215

SP - 45

EP - 57

JO - Topology and its Applications

JF - Topology and its Applications

ER -

Higson compactification and dimension raising

Abstract

Keywords

ASJC Scopus subject areas

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