Professor Alexandru I. Suciu MATH 4565 · Topology Spring 2018

Course Information

 Course: MATH 4565 · Topology Web site: web.northeastern.edu/suciu/MATH4565/utop.sp18.html Instructor: Prof. Alex Suciu,   a.suciu@northeastern.edu Time and Place: Tuesday & Friday 1:35–3:15 pm, in 20 Stetson East Office Hours: Tuesday & Friday 3:30pm–4:30pm in 505A LA, or by appointment TA: Saif Sultan,   sultan.s@husky.neu.edu Textbook: Topology (2nd Edition) by James R. Munkres, Pearson, 2018 Grade: Based 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, as well as their "local" versions. We also introduce several constructions of spaces, including identification spaces. 2. Fundamental Group and Covering Spaces This part of the course is a brief introduction to Geometric Topology. It starts with Poincaré's definition of the fundamental group of a space, and various methods to compute it, such as the Seifert-van Kampen theorem. It proceeds with the classification of surfaces, and a detailed study of covering spaces. Applications include the Brouwer fixed point theorem, the Borsuk-Ulam theorem, and the Nielsen-Schreier theorem.

Homework Assignments

Assignment Chapter Pages Problems
Homework 1
Due Jan. 30
Munkres 2.13 83 1, 2
Munkres 2.17 100–101 2, 6, 14
Munkres 2.20 126 1(a)
Homework 2
Due Feb. 9
Munkres 2.16 92 5
Munkres 2.17 100-101 3, 9, 13
Munkres 2.18 111-112 3, 10
Homework 3
Due Feb. 20
Munkres 3.23 152 4, 9
Munkres 3.24 158 3, 8, 9, 10
Homework 4
Due March 2
Munkres 3.25 162 4, 5(a), 6
Munkres 3.26 172 1, 3, 7
Homework 5
Due April 3
Munkres 2.22 144-145 2(a), 3
Munkres 2.22 supplement 146 5(b)-(c)
Munkres 9.51 330 3(c)-(d)
Munkres 9.58 366 1, 5&6
Homework 6
Due April 13
Munkres 9.52 335 3, 6
Munkres 9.53 341 3, 4, 5
Munkres 9.54 348 8

Exams

 Department of Mathematics Office: 505A Lake Hall Northeastern University Phone: (617) 373-5635 Boston, MA, 02115 Email: a.suciu@northeastern.edu