Course instructor: Melissa Zhang
Course TA: Ian Sullivan
Instructor Office Hours: MSB 3240, M 4-5pm, F 2-3pm. See Canvas announcements for occasional modifications.
TA Office Hours: MSB 3240, W 4-5. See Canvas announcements for occasional modifications.
Textbook: Algebraic Topology by Allen Hatcher [Online Version]
Department syllabus for Mat215A: [link]
Question 3: You may assume that X is locally path-connected.
Question 3: "Universal covering space" in this problem means "simply-connected covering space".
Question 4: Should we assume that the CW complex X is finite-dimensional? Indeed the equation $\chi(\tilde X) = k \chi(X)$ only makes sense if $X$ is a finite CW complex, but for the rest of the problem you should not a priori assume that $X$ is finite-dimensional.
Question 4(a): May we use Proposition A.2 in Hatcher? You are welcome to, but your solution need not be too pedantic; the intended solution does not refer to this proposition (though it perhaps implicitly uses it). For this exam, it is enough to describe the CW structure on the covering space, with a brief justification of why this CW complex indeed recovers the covering space.