The simplest examples of geodesic metric spaces that are not manifolds are provided by metric graphs, which we introduced in (1.9). In this section we shall study their higher dimensional analogues, M k —polyhedral complexes. Roughly speaking, an M k—polyhedral complex is a space that one gets by taking the disjoint union of a family of convex polyhedra from M k n and gluing them along isometric faces (see (7.37)). The complex is endowed with the quotient metric (5.19). The main result in this chapter is the following theorem from Bridson’s thesis [Bri91] (see (7.19)).
KeywordsSimplicial Complex Geodesic Segment Cubical Complex Geodesic Space Barycentric Subdivision
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