**Math 540: Introduction to Algebraic Topology I**

**Fall 2020**

**Instructor:** Kristen Hendricks

**Email:** kristen. hendricks at rutgers.edu

**Office Hours:** M 3:30-4:30 W 4:30-5:30, or by appointment. Office hours take place at Zoom Meeting ID 995 9623 4738. The password is a chain with trivial boundary. Please email me if you are having trouble getting into office hours.

A printable copy of the syllabus is here.

**Location and Time**: MW 1:40-3:00, over Zoom (via Canvas integration).

**Prerequisites**: Point-set topology and abstract algebra (groups, rings, fields).

**Topics**: This is a standard first course in algebraic topology. We will cover the fundamental group, covering spaces, and singular, simplicial, and cellular homology and cohomology. Along the way we will prove some rather nice applications..

**Notes**: My lecture notes will be posted here and on Canvas shortly after class. Lecture videos will also be uploaded to Canvas.

**Homework**: Homework exercises for each week will be posted some time before the start of Monday’s lecture, and the file will be shared in class. Registered students are expected to demonstrate having solved roughly half the homework exercises. (Acceptable methods of demonstrating this include handing in your written solutions, writing solutions in the class OneNote notebook, and coming to office hours and explaining your work.)

**Text**: The textbook for this course is A. Hatcher’s
Algebraic Topology, which is available for free on his website. It is a very friendly textbook; doing the reading before coming to lecture is advised. We will be covering roughly Chapters 0-3, excluding the special topics.
Other good books on the same material include:

- J. P. May, A Concise Course in Algebraic Topology. Available at May's website.
- W. Massey, Algebraic Topology: An Introduction and A Basic Course in Algebraic Topology.
- J. Munkres, Elements of Algebraic Topology and Topology.
- E. Spanier, Algebraic Topology.
- A. Fomenko and D. Fuchs, Homotopical Topology. Available through Rutgers SpringerLink.

**Assignments**

Homework will be posted here weekly.