MATH 751: INTRODUCTORY TOPOLOGY, I
TR 2:30–3:45 PM in Van Vleck B113
with Autumn Kent

Office: Van Vleck 615
Office hours: Thursdays 1:30–2:30, by appointment, or stop by.

Exam dates:
Take home exam, 10/13 – 10/18
Take home exam, 12/15 – 12/19
Problem Sessions:
TBD.
Main text:
Algebraic topology, by Allen Hatcher.

Supplementary texts (on reserve in library):
A Basic Course in Algebraic Topology, by William S. Massey

Classical Topology and Combinatorial Group Theory, by John Stillwell

Supplementary materials:

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%).

The purpose of the course is to prepare you for the Qualifying Exam in Geometry and Topology. Final letter grades will be allocated according to a crude scheme based on your numerical performance: an A means that it is likely that you will pass the qualifying exam, a B means that is not likely that you will pass the qualifying exam, and an F means that you did little to no work in the course. I will not assign any other letter grades.






Homework:



HW5, never due.
Hatcher:
Section 2.1: 4, 5, 8, 9, 11, 22, 29
Section 2.2: 9, 12, 28, 29, 32
HW4, due 11/22.
Hatcher:
Section 1.3: 12, 14, 16, 18, 20, 25, 29
HW3, due 11/15.
Hatcher:
Section 1.2: 10, 11, 20
Section 1.3: 3, 4, 9, 10

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.
HW2, due 10/11.
Hatcher:
Section 1.1: 1, 3, 5, 6, 8, 12, 13, 16, 17
HW1, due Tuesday 9/20.
Hatcher:
Chapter 0: 1, 2, 3, 5, 6, 9, 10, 12, 14, 16, 20, 23