Tuesdays and Thursdays 1:30-2:45 SC 507
This class is an introduction to point-set and algebraic topology. Some topics we may cover include topological spaces, connectedness, compactness, metric spaces, normal spaces, the fundamental group, homotopy type, covering spaces, quotients and gluing, and simplicial complexes.
Instructor: Brooke Ullery (bullery@math, office SC 503, office hours Mondays and Thursdays 11-noon and by appointment)
Course assistants: Filippos Sytilidis (fsytilidis@college), Natalia Pacheco-Tallaj (pachecotallaj@college), and Daniel Qu (dqu@college), office hours Monday 8pm-10pm at math night.
Text: "Topology: A First Course" by James Munkres.
Homework: Problem sets will be assigned weekly (mostly due Tuesdays). I encourage you to work on the problems together, but you must turn in your own solutions and list the names of your collaborators.
Exams: There will be one take-home midterm (handed out in class Oct 23, due Oct 25). The take-home final can be picked up 12/7 between 12 and 2 and handed in on 12/10 by 2.
Grading: Homework: 60%, Exams: 20% each
Problem set 1 (tex file), due September 11
Problem set 2 (tex file), due September 18
Problem set 3 (tex file), due September 25
Problem set 4 (tex file), due October 2
Problem set 5 (tex file), due October 9
Problem set 6 (tex file), due October 16
Problem set 7, part 1 (tex file), due October 23
Problem set 7, part 2 (tex file), due October 30
Problem set 8 (tex file), due November 8
Problem set 9 (tex file), due November 15
Problem set 10 (tex file), due November 27
Problem set 11 (tex file), due December 6
You can find the lecture notes from class here. I'll post each section after we've covered it, so there may be some notes covering multiple days. Warning: There will inevitably be typos in the notes!
Section 1: What is topology?
Section 2: Motivating example -- metric spaces
Section 3: Topological spaces
Section 4: Bases and lots of examples
Section 5: Continuity and homeomorphisms
Section 6: Closed sets and limit points
Section 7: Topologies on infinite products
Section 8: Connected spaces
Section 9: Compact spaces
Section 10: Compactness in metric spaces
Section 11: Compactifications and local compactness
Section 12: Categories, groupoids, and functors
Section 13: Paths
Section 14: The fundamental group
Section 15: Covering spaces and path lifting
Section 16: Quotients and gluing
Section 17: Global topology 1 - Fixed points and retractions
Section 18: Global topology 2 - Antipodes and Borsuk-Ulam
Section 19: Deformation retracts and homotopy equivalence
Section 20: Introduction to van Kampen and more fundamental group calculations
Section 21: Equivalence of covering spaces
Section 22: Crash course in free products of groups
Section 23: The Seifert-van Kampen Theorem and more calculations
Upcoming topics: None :(
Midterm -- Midterm solutions
Final exam -- Final exam solutions