J. Brazas, Unwinding paths in the plane to form an R-tree

If we "unwind" all paths in a graph up to backtracking, we end up forming a tree that serves as the universal covering space of the graph. In a similar way, we can unwind paths in a more complicated one-dimensional space like the Sierpinski Carpet. However, in this case, we end up forming an R-tree, which serves as a kind of generalized universal covering space. In this talk, I'll discuss whether or not there exists a suitable notion of "thin" or "one-dimensional" homotopy that makes it possible to unwind all paths in the plane (up to one-dimensional backtracking) to form an R-tree. The answer settles a problem posed by Jerzy Dydak and has a variety of applications to covering space theory and it's generalizations.