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Combinatorial \({\mathbb{R}}\)-trees as generalized Cayley graphs for fundamental groups of one-dimensional spaces

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Abstract

In their study of fundamental groups of one-dimensional path-connected compact metric spaces, Cannon and Conner have asked: Is there a tree-like object that might be considered the topological Cayley graph? We answer this question in the positive and provide a combinatorial description of such an object.

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Correspondence to Hanspeter Fischer.

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Fischer, H., Zastrow, A. Combinatorial \({\mathbb{R}}\)-trees as generalized Cayley graphs for fundamental groups of one-dimensional spaces. Geom Dedicata 163, 19–43 (2013). https://doi.org/10.1007/s10711-012-9734-0

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  • DOI: https://doi.org/10.1007/s10711-012-9734-0

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