 
Summary: COLLOQUIUM
University of Regina
Department of Mathematics and Statistics
Speaker: Jeff Strom (Western Michigan University)
Title: Complexity with Respect to Good Spaces
Date: Friday, January 16, 2004
Time: 15:30
Place: Math & Stats Lounge (CW 307.18)
Abstract
A closed class is a collection of topological spaces which is closed
under (weak) homotopy equivalences and the homotopytheoretical ver
sion of 'taking the union' (known as homotopy colimit). For a space
A, we may form C(A), the smallest closed class which contains A. If
X C(A), then we can ask: if we start with just copies of A, then
how many homotopy colimits are required to obtain X? The answer
is called the Acomplexity of X, and is denoted A(X). In principle,
A(X) could be a very large ordinal number.
On the other hand, certain closed classes C(A) have an additional
property: if F E B is a fibration sequence with F, B C(A),
then E C(A) as well. We call any space A such that C(A) has this
