A representation theorem for end spaces of infinite graphs

Jan Kurkofka; Max Pitz

doi:10.48550/arXiv.2111.12670

A representation theorem for end spaces of infinite graphs

Jan Kurkofka, Max Pitz

Mathematics

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Abstract

End spaces of infinite graphs sit at the interface between graph theory, group theory and topology. They arise as the boundary of an infinite graph in a standard sense generalising the theory of the Freudenthal boundary developed by Freudenthal and Hopf in the 1940's for infinite groups.

A long-standing quest in infinite graph theory with a rich body of literature seeks to describe the possible end structures of graphs by a set of low-complexity representatives. In this paper we propose a solution to this fifty-year-old problem by showing that every end space is homeomorphic to the end space of some (uniform graph on a) special order tree.

Original language	English
Publisher	arXiv
DOIs	https://doi.org/10.48550/arXiv.2111.12670
Publication status	Published - 2 Mar 2023

Bibliographical note

V2 adds a moreover-part to Theorem 3.2. V3 has updated references

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A representation theorem for end spaces of infinite graphs

Abstract

Bibliographical note

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