Skip to main content
Photo of Dennis Garity

Dennis J. Garity

Emeritus Professor
Department of Mathematics

Dennis J. Garity

Emeritus Professor
Department of Mathematics

Background

Education

PhD., Wisconsin, Madison, 1980

M.S., Wisconsin, Madison, 1976

Research

Research Field 

Geometric Topology, Dimension Theory and Topological Manifolds

Research Description

Garity's current 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. 

Research Group 

Geometry/Topology