MATH 751: INTRODUCTORY TOPOLOGY, I
TR 2:30–3:45 PM in Van Vleck B309 with Autumn Kent Office: Van Vleck 615 Office hours: Wednesday 2–4, by appointment, or try stopping by. Exam dates: Take home exam, 10/23 – 10/26Problem Sessions: 10/1 at 4:30pm in Van Vleck B219Main text: Algebraic topology, by Allen Hatcher. Supplementary texts (on reserve in library): A Basic Course in Algebraic Topology, by William S. Massey Supplementary materials: Midterm 1 (.pdf) (.tex) Grades: There will be two midterm exams (designed as miniature qualifying exams), and regular homework (on the right side of this page). Your final grade in the course will be based on your performance on these three items, weighted roughly as Homework (30%), Midterm #1 (30%), Midterm #2 (40%). |
Homework:
HW6, due 12/13.
Hatcher: Section 2.1: 4, 5, 8, 9, 11, 22 HW5, due 11/20.
1. Show that action of \(\Gamma[2] = \mathrm{ker}(\mathbb{P}\mathrm{SL}_2(\mathbb{Z}) \to \mathbb{P}\mathrm{SL}_2(\mathbb{Z}/2\mathbb{Z}))\) on the upper half–plane \(\mathbb{H}\) is a covering space action.Hatcher: Section 1.3: 12, 14, 16, 18, 20, 25, 29 HW4, due 11/06.
1. Prove Lemma 1: The only compact connected surface with boundary that possesses no nonseparating arc is the disk.Hatcher: Section 1.2: 16, 19 HW3, due 10/18.
Hatcher: Section 1.1: 16, 17 HW2, due 10/04.
Hatcher: Chapter 0: 22 HW1, due 09/25.
Hatcher: Chapter 0: 1, 2, 3, 5, 6, 9, 10, 12, 14, 16, 20, 23 |