Research

Research Field

Geometric Topology, Dimension Theory and Topological Manifolds

Research Description

Garity's research is focused on properties of embeddings of Cantor sets in Euclidean spaces, focusing on embeddings in R^3. Cantor sets often arise as limit sets or invariant sets of dynamical systems. The complements of such Cantor sets in R^3 are 3-manifolds with a rich end structure. The possible types of embeddings of these sets in R^n can provide information about possible dynamical systems and about the end structure of manifolds. Recent examples include nonstandard embeddings with simply connected complement, nonstandard embeddings that are rigid, and nonstandard embeddings with both properties.

Education

Ph.D., Wisconsin, Madison, 1980

M.S., Wisconsin, Madison, 1976

Research areas