The fundamental group of a locally finite graph with ends-a hyperfinite approach

• Autorzy: Isaac Goldbring , Alessandro Sisto
• Języki publikacji: EN

Abstrakty

EN

The end compactification |Γ| of a locally finite graph Γis 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 show how to recover the standard description of π₁(|Γ|) given by Diestel and Sprüssel (2011). Finally, we give some applications of our result, including a short proof that certain loops in |Γ| are non-nullhomologous.

Kategorie tematyczne

• 03H05: Nonstandard models in mathematics
• 14F35: Homotopy theory; fundamental groups
• 05C63: Infinite graphs

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 232
• Numer: 1
• Strony: 21-39

Daty

wydano

2016

Twórcy

autor

Isaac Goldbring

• Department of Mathematics, Statistics,, and Computer Science, University of Illinois at Chicago, Science and Engineering Offices (M/C 249), 851 S. Morgan St., Chicago, IL 60607-7045, U.S.A.

autor

Alessandro Sisto

• Department of Mathematics, ETH Zürich, HG J 14.4, Rämistrasse 101, 8092 Zürich, Switzerland

Identyfikatory

DOI

10.4064/fm232-1-2