Combinatorial -trees as generalized Cayley graphs for fundamental groups of one-dimensional spaces

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 ob...

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Bibliographic Details
Published in:Geometriae dedicata 2013-04, Vol.163 (1), p.19-43
Main Authors: Fischer, Hanspeter, Zastrow, Andreas
Format: Article
Language:English
Subjects:
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
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Summary: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.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-012-9734-0