Alex Wang
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I am a mathematics student at the University of Michigan.
Is it a mug? Or a donut?
Algebraic Topology Reading Group
Group Meets: Tuesday 5:30 PM  7:00 PM, EH2866 Cancelled due to COVID19 concerns.
Text: We will roughly follow either
Both of these are available for free online, through the links above. Other resources that may be useful are both Topology by James R. Munkres and Elements of Algebraic Topology by James R. Munkres. Another very useful resource is Ben Gould's notes for Math 592 at the University of Michigan, which can be found here.
Prerequisites: We will assume a first course in pointset topology as well as basic algebra (groups, etc).
Structure: The structure of the reading group will be as follows: every week, we will select a portion of reading to work through. In addition, we will designate one person (or group) to lead the discussion, by giving a short presentation on the material. Finally, the discussion leaders will TeX the notes to the weekly discussion, which everyone is free to contribute to and edit.
Notes: Notes from our reading group can be found here. Notes will be compiled and uploaded here on Thursdays following each meeting. These notes are highly incomplete, very messy, and likely will not be reorganized.
Schedule
Italicized topics denote reading if time permits. Important italicized topics will be moved to the next week. Note that H denotes Hatcher, M denotes May, and G denotes Ben Gould's notes.

Monday, January 20: NO MEETING (MLK Day). Read Chapter 0 of Hatcher.

Monday, January 27: The Fundamental Group (H2128), The Fundamental Group of the Circle (H2931), Other examples of the Fundamental Group (H3134)
 Discussion Leader: Raviv Sarch
 Status: We talked about homotopy, path homotopy, and defined the fundamental group. We then defined covering spaces and lifts in order to prove that the fundamental group of the circle is the integers.

Tuesday, February 4: Category Theory Primer (M1317)
 Discussion Leader: Alex Wang
 Status: We defined a category, then talked about terminal objects and isomorphisms. We then talked about functors, universal properties, limits, and adjunctions.

Tuesday, February 11: The Van Kampen Theorem (M1719, H4046)
 Discussion Leader: Steven Schaefer
 Status: We defined the free product of groups, and stated and proved Van Kampen's Theorem following the proof in Hatcher. We then computed the fundamental group of a few example spaces.

Tuesday, February 18: Covering Spaces (H5676, M2122, G1623)
 Discussion Leader: Vikram Mathew
 Status: We defined a covering space, and proved results about covering spaces, homotopy, and lifts. We then constructed the universal cover of a space.

Tuesday, February 25: Simplicial Homology (H102107, M126128, G2730)
 Discussion Leader: Joe Carter
 Status: We defined a simplex and a Delta complex, and worked through some examples. We then defined simplicial homology.
Tuesday, March 3: NO MEETING (Spring Break).

Tuesday, March 10: Singular Homology (H107113, M123128, G3033)
 Discussion Leader: Ethan Mook
 Status: We defined the singular nsimplex, and used it to define singular homology. We then showed that homotopic maps induce the same maps on homology.

Unfortunately, the reading group has been cancelled due to COVID19 concerns.