Exam I will be in Room 809 PHSC on Wednesday, February 23, 2005, from 7:00-9:00 p. m. The exam is closed-book and closed-notes; that is, all you will need is something with which to write.

The exam will emphasize the classifcation of surfaces, both the general classification, and the use of Euler characteristic and orientability to classify surfaces algebraically. Be familiar with sliding handles and the ideas of the proof of the classification theorems, other than barycentric subdivisions of triangulations.

In addition to handle structures and the classification of surfaces, the topics include (but are not limited to) the following:

1.	definition of a collar of the boundary of a manifold
2.	homotopy, isotopy, ambient isotopy, path homotopy
3.	contractible spaces
4.	the canonical example of an application of fundamental groups: proving that the circle is not a retract of the disk (know this perfectly, the question will be ``Use the facts that &pi1(S1,s0)= Z and &pi1(D2,s0)= {0}, together with the functorial properties of the induced homomorphism, to prove that the circle is not a retract of the disk.'')
5.	path homotopy, path product, definition of the fundamental group

The following topics will not appear on the exam:

1.	the Invariance of Domain theorem
2.	the ``beggar's isotopy'' example
3.	the exact statement of the handle sliding lemma, and its proof
4.	the proof using the Disk Lemma that two boundary components that are spheres (such as boundary circles of surfaces) can be interchanged using a homeomorphism of the manifold
5.	barycentric subdivision, using a triangulation to obtain a handle structure on a surface