Place: Fields Institute, Room 230
Date and time: Friday 06 February, 13:30-15:00
Title: A complete classification of homogeneous plane compacta
Abstract: In this topology talk, we will discuss homogeneous spaces in the plane $R^2$. A space X is homogeneous if for every pair of points in X, there is a homeomorphism of X to itself taking one point to the other. Kuratowski and Knaster asked in 1920 whether the circle is the only connected homogeneous compact space in the plane. Explorations of this problem fueled a significant amount of research in continuum theory, and among other things, led to the discovery of two new homogeneous spaces in the plane: the pseudo-arc and the circle of pseudo-arcs. I will describe our recent result which implies that there are no more undiscovered homogeneous compact spaces in the plane. This is joint work with Lex Oversteegen of the University of Alabama at Birmingham.