A Cayley graph consists of vertices and edges, and distances are defined for elements of a given group. Then what about the edges? It is stated that "the 1-skeleton of a Cayley complex is a Cayley graph." Then, are the edges 1-cells attached between pairs of points that are of distance 1 so that distances for points on the edges can be defined? Moreover, is it for this reason that (topological) paths and loops, which are continuous functions defined on an interval $I \subset R$, can be defined regarding fundamental groups?
2026-03-27 06:51:20.1774594280
Cayley graph as a 1-skeleton
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