|
Professor Alexandru I. Suciu
|
|
MTH 3105 Topology I
|
Fall 2001
|
Course Information
Course Description
This course provides an introduction to Topology, requiring only some elementary background in Analysis. Time permitting, the following topics will be covered:
|
|
Topological Spaces and Continuous Functions
|
|
|
Compactness and Connectedness
|
|
|
The Fundamental Group
|
|
|
The Seifert-van Kampen Theorem
|
|
|
Classification of Surfaces
|
|
|
Classification of Covering Spaces
|
|
|
Applications to Group Theory
|
The first (shorter) part of the course treats General Topology. The objects of study are metric and topological spaces. The main properties that are studied are connectedness and compactness. We also introduce several constructions of spaces, and study the invariance of various properties under topological equivalence.
The second part of the course treats the basics of Algebraic and Geometric Topology. It starts with the fundamental group of a space, 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.
For more information, including past exams and class projects, see this older syllabus. You may also want to look at some past qualifying exams in Topology, based in large part on the material covered in this course.
Homework Assignments
Homework
|
Section
|
Page
|
Problems
|
1.
|
Section 2.16
|
Page 92
|
Problems 3, 4
|
Section 2.17
|
Page 101
|
Problems 11, 12, 13
|
Section 2.18
|
Pages 111--112
|
Problems 3, 10
|
Section 3.23
|
Page 152
|
Problems 2, 5, 9
|
|
2.
|
Section 3.24
|
Page 158
|
Problems 2, 3, 9, 10
|
Section 3.25
|
Page 162
|
Problems 5, 6, 7
|
Section 3.26
|
Page 171
|
Problems 6, 7, 8
|
|
3.
|
Section 2.22
|
Pages 144--145
|
Problems 2, 3
|
Section 9.51
|
Page 330
|
Problems 3
|
Section 9.52
|
Pages 334--335
|
Problems 2, 3, 4, 6
|
Section 9.53
|
Pages 341
|
Problems 3, 5, 6
|
|
4.
|
Section 9.54
|
Page 348
|
Problems 5, 8
|
Section 9.55
|
Page 353
|
Problem 2
|
Section 9.57
|
Page 359
|
Problems 2, 3
|
Section 9.58
|
Page 367
|
Problem 9(e)
|
|
5.
|
Section 9.58
|
Page 366
|
Problem 2
|
Section 11.69
|
Page 425
|
Problems 1, 3
|
Section 11.70
|
Page 433
|
Problems 1, 2
|
Section 12.74
|
Pages 453--454
|
Problems 1, 2, 6, 7
|
Section 12.76
|
Page 457
|
Problems 4
|