MATH 4565 Topology

  • Last modification date Updated On December 4, 2024

Fall 2024

Course Information

CourseMATH 4565 · Topology
InstructorAlex Suciu
Course Web Sitehttps://suciu.sites.northeastern.edu/courses/math4565-fall2024
Time and PlaceTuesday & Friday 9:50am–11:30am in Cahners Hall 8
Office435 LA – Lake Hall
Emaila.suciu@northeastern.edu
Office HoursWednesday 10:30 am–11:30 am & Friday 1:45 pm–2:45 pm, or by appointment
Prerequisites:MATH 3150 – Real Analysis
TextbookIntroduction to Topological Manifolds, Second Edition, by John M. Lee, Graduate Texts in Mathematics, vol. 202, Springer, 2011.
Additional booksTopology (2nd Edition), by James R. Munkres, Pearson, 2018.
Algebraic Topology, by Allen Hatcher, Cambridge University Press, 2001 (pdf file).
GradeBased on problem sets (50%), midterm exam (20%), and final exam (30%). It is expected that you will work on the problem sets together; however, they must be written up separately.

Course Description

This course provides an introduction to the concepts and methods of Topology. It consists of two, inter-connected parts.

1. Topological Spaces and Continuous Maps

This part of the course serves as an introduction to General Topology. The objects of study are topological spaces and continuous maps between them. Key is the notion of homeomorphism, which leads to the study of topological invariants. The main properties that are studied are connectedness, path connectedness, and compactness. We also introduce several constructions of spaces, including identification spaces, and discuss topological manifolds and topological groups.

2. Fundamental Group and Covering Spaces

This part of the course is a brief introduction to Geometric Topology. It starts with the definition of the fundamental group of a space, and various methods to compute it, such as the Seifert-van Kampen theorem. It proceeds with an introduction to the theory of covering spaces.

Assignments and Exams

  • Assignment #1 (due September 24): Exercise 2.4 (a),(b) · Exercises 2.21 & 2.23 · Problem 2-2 · Problem 2-5 (arbitrary spaces X and Y allowed), Problem 2-17.
  • Assignment #2 (due October 11): Exercise 2.32 · Exercise 2.35 · Problem 2-10 · Problem 2-11 · Problem 3-6
  • Assignment #3 (due October 23): Exercise 3.45 · Exercise 3.63 (parts a, b, c) · Problem 3-5 · Problem 3-13 (for quotient maps) · Problem 4-1
  • Midterm Exam (due November 5)
  • Assignment #4 (due November 17)
  • Final Exam (due December 13)

Course Materials

Handouts

Past Courses