
\begin{abstract}
The following are notes to help me prepare for the University of Arizona math
department's geometry-topology qualifier in August 2006.
(My complex-analysis notes are in a separate document.)
The list of topics is based on, but presented in a different order from, Prof.
Doug Pickrell's 2005-2006 geometry-topology course (Math 534A-B).
(Notes for the complex-analysis portion of the qualifier are in a separate
paper.)
References are taken from
Lang's \emph{Algebra},
Spivak's \emph{Calculus on Manifolds},
Lee's
\emph{Introduction to Topological Manifolds} and
\emph{Introduction to Smooth Manifolds},
and other sources.

My intention is to gather together precise definitions and thorough examples in
a form that is concise and well-organized, or at least well-organized.  This
document is a work perpetually in progress.

Note as of Nov. 2006:  Any of you who have been following this project will
likely have noticed I've not made any updates in a while.  While these notes
were originally an act of desperation, I've since found Lee, Boothby, and
especially Frankel which provide the kind of organized, coherent treatments I'd
been longing for.  At some point I'll include more qualifier-prep material, but
at the moment, the urgency for finishing these notes is greatly abated.

\end{abstract}
