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Dendrites and path-homotopies

Curtis Kent ⟨curtkent@mathematics.byu.edu⟩

Abstract:

In a one-dimensional space, any nullhomotopic loop factors through a dendrite. Analogously, we can say that two paths f and g, with the same endpoints, are equivalent if fg factors through a loop in a dendrite, where g is the path g traversed backwards. We will show that the equivalence relation generated by this relation is the same as the path-homotopy and discuss its consequences.

This is joint work with Greg Conner, Jeremy Brazas, and Paul Fabel.

Status: Accepted

Collection: Continuum Theory

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