Topology, by Munkres
  Professor Alexandru I. Suciu
  		Topology, by Munkres
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

* Handouts

* Exams

Department of Mathematics  Office:  505A Lake Hall 
Northeastern University Phone:  (617) 373-5635 
Boston, MA, 02115  Email:  a.suciu@northeastern.edu
Home Started:  November 23, 2017
Last modified:  April 29, 2018
          web.northeastern.edu/suciu/MATH4565/utop.sp18.html