
Professor Alexandru I. Suciu


MATH 4565 · Topology

Spring 2018

Course Information
Course Description
This course provides an introduction to the concepts and methods of Topology. It consists of two interconnected 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 Seifertvan Kampen theorem. It proceeds with the classification of surfaces, and a detailed study of covering spaces. Applications include the Brouwer fixed point theorem, the BorsukUlam theorem, and the NielsenSchreier 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

100101

3, 9, 13

Munkres 2.18

111112

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

144145

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
