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University of Regina Department of Mathematics and Statistics

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)
A closed class is a collection of topological spaces which is closed
under (weak) homotopy equivalences and the homotopy-theoretical 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 A-complexity 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


Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina


Collections: Mathematics