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math.MG2013★ 1 cited
Essential Circles and Gromov-Hausdorff Convergence of Covers
Conrad Plaut, Jay Wilkins
We give various applications of essential circles (introduced in an earlier paper by the authors) in a compact geodesic space X. Essential circles completely determine the homotopy…
math.MG2012
Discrete Homotopy Theory and Critical Values of Metric Spaces
Jim Conant, Victoria Curnutte, Corey Jones +4
Utilizing the discrete homotopy methods developed for uniform spaces by Berestovskii-Plaut, we define the critical spectrum Cr(X) of a metric space, generalizing to the non-geodesi…