Quotients of R-trees under group actions with unique path lifting contain no discs, implying that maps of manifolds with unique path lifting are covering maps, via the result that path homotopies are generated by one-dimensional backtracking.
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On R-trees, homotopies, and covering maps
Quotients of R-trees under group actions with unique path lifting contain no discs, implying that maps of manifolds with unique path lifting are covering maps, via the result that path homotopies are generated by one-dimensional backtracking.