A tree-of-tangles theorem for infinite tangles

Ann-Kathrin Elm; Jan Kurkofka

doi:10.1007/s12188-022-00259-1

A tree-of-tangles theorem for infinite tangles

Ann-Kathrin Elm, Jan Kurkofka^*

^*Corresponding author for this work

Mathematics

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Abstract

Carmesin has extended Robertson and Seymour’s tree-of-tangles theorem to the infinite tangles of locally finite infinite graphs. We extend it further to the infinite tangles of all infinite graphs. Our result has a number of applications for the topology of infinite graphs, such as their end spaces and their compactifications.

Original language	English
Pages (from-to)	139–178
Number of pages	40
Journal	Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
Volume	92
Issue number	2
DOIs	https://doi.org/10.1007/s12188-022-00259-1
Publication status	Published - 29 Nov 2022

Keywords

Infinite tree of tangles
End
Ultrafilter tangle
Tree set
Critical vertex
set
distinguish
Efficiently
Collectionwise normal

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Cite this

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AB - Carmesin has extended Robertson and Seymour’s tree-of-tangles theorem to the infinite tangles of locally finite infinite graphs. We extend it further to the infinite tangles of all infinite graphs. Our result has a number of applications for the topology of infinite graphs, such as their end spaces and their compactifications.

KW - Infinite tree of tangles

KW - End

KW - Ultrafilter tangle

KW - Tree set

KW - Critical vertex

KW - set

KW - distinguish

KW - Efficiently

KW - Collectionwise normal

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A tree-of-tangles theorem for infinite tangles

Abstract

Keywords

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