4 papers
Uncountable groups and the geometry of inverse limits of coverings
Gregory Conner, Wolfgang Herfort, Curtis Kent +1
In this paper we develop a new approach to the study of uncountable fundamental groups by using Hurewicz fibrations with the unique path-lifting property (lifting spaces for short)…
Asymptotic cones and boundaries of CAT(0) groups
Curtis Kent, Russell Ricks
It is well known that the Tits boundary of a proper cocompact CAT(0) space embeds into every asymptotic cone of the space. We explore the relationships between the asymptotic cones…
Homotopy type of planar continua
Curtis Kent
We prove that the homotopy type of a map from a Peano continuum into a planar or one-dimensional space is determined by the induced homomorphism of fundamental groups. This provide…
Inverse Limits of Finite Rank Free Groups
Gregory Conner, Curt Kent
We will show that all inverse limits of finite rank free groups index by the natural numbers are isomorphic either to a finite rank free group or to a fixed universal group. In oth…