The fundamental group of a locally finite graph with ends–-a hyperfinite approach
نویسندگان
چکیده
منابع مشابه
The Fundamental Group of a Locally Finite Graph with Ends- a Hyperfinite Approach
The end compactification |Γ| of the locally finite graph Γ is the union of the graph and its ends, endowed with a suitable topology. We show that π1(|Γ|) embeds into a nonstandard free group with hyperfinitely many generators, i.e. an ultraproduct of finitely generated free groups, and that the embedding we construct factors through an embedding into an inverse limit of free groups. We also sho...
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We characterize the fundamental group of a locally finite graph G with ends combinatorially, as a group of infinite words. Our characterization gives rise to a canonical embedding of this group in the inverse limit of the free groups ⇡1(G 0) with G0 ✓ G finite.
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We characterize the fundamental group of a locally finite graph G with ends, by embedding it canonically as a subgroup in the inverse limit of the free groups π1(G ′) with G′ ⊆ G finite. As an intermediate step, we characterize π1(|G|) combinatorially as a group of infinite words.
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We show that the topological cycle space of a locally finite graph is a canonical quotient of the first singular homology group of its Freudenthal compactification, and we characterize the graphs for which the two coincide. We construct a new singular-type homology for non-compact spaces with ends, which in dimension 1 captures precisely the topological cycle space of graphs but works in any di...
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This paper is intended as an introductory survey of a newly emerging field: a topological approach to the study of locally finite graphs that crucially incorporates their ends. Topological arcs and circles, which may pass through ends, assume the role played in finite graphs by paths and cycles. This approach has made it possible to extend to locally finite graphs many classical theorems of fin...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2016
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm232-1-2