**Title:** A-Complexity and Good Spaces

**Speaker:** Professor Jeff Strom

**Speaker Info:** Western Michigan

**Brief Description:**

**Special Note**:

**Abstract:**

(Joint work with Michele Intermont)A closed class is a class of spaces which is closed under weak equivalences and pointed homotopy colimits. Every space $A$ generates a closed class $\mathcal{C}(A)$; the $A$-complexity of a space $X\in \mathcal{C}(A)$ is the minimum number of homotopy colimit operations required to construct $X$ starting with wedges of copies of $A$.

A space $A$ is called a good space if $\mathcal{C}(A)$ is closed under extensions by fibrations (any sphere $S^n$ is an example of such a space).

We will derive some useful estimates of the $A$-complexity. Then we will turn our attention to finding some special properties enjoyed by good spaces, including a characterization of good spaces. Finally, we will tie these two strands together, by showing that, if $A$ is a good space, then there is a countable bound on the $\s A$ complexity of every space that is \textit{indpendent of both $X$ and $A$}.

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