Abstract

In Definition 2.0.3 we define an equivalence relation on paths such that two paths into a space X are related if doing the first, then the second backwards factors as a loop through a dendrite. This equivalence relation induces a group structure L(X) on a large subset of the loop space of X, namely all loops that have a unique reduced representative. We show that certain continuous maps induce a homomorphism between dentropy groups and that projection from three-dimensional real space to two-dimensional real space does not induce a homomorphism on dentropy groups.. We show that dentropy groups are locally free. For any finitely generated subgroup G of X, there exists a one-dimensional space Y with a map that induces an isomorphism from L(Y) to G, such that every path to X lifts to Y and every path with a unique reduced representative lifts uniquely.

Degree

College and Department

Computational, Mathematical, and Physical Sciences; Mathematics

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