Metric Geometry and Random Discrete Morse Theory
نویسندگان
چکیده
How to put a metric on a given simplicial complex? One way is to declare all edges to have unit length, and to regard all triangles as equilateral triangles in the Euclidean plane. This yields the equilateral flat metric, also known as regular metric. Many other options are possible; for example, one can assign different lengths to the various edges. The metric is called acute (resp. non-obtuse) if all dihedral angles in each simplex are less than 90 degrees (resp. at most 90 degrees). Clearly, equilateral implies acute, which in turn implies non-obtuse.
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