# Math 554: Foundations of Topology 2

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## Contents

## Catalog Information

### Title

Foundations of Topology 2.

### (Credit Hours:Lecture Hours:Lab Hours)

(3:3:0)

### Prerequisite

Math 553 or instructor's consent.

### Description

Fundamental group, retractions and fixed points, homotopy types, separation theorems, classification of surfaces, Seifert-van Kampen Theorem, classification of covering spaces, and applications to group theory.

## Desired Learning Outcomes

Students should gain a familiarity with surfaces, fundamental group, and covering spaces.

### Minimal learning outcomes

- The Fundamenatal Group
- The topology of the plane
- Jordan Curve Theorem

- Seifert-van Kampen Theorem
- Classification of Surfaces
- Classification of Covering Spaces
- Group Theory
- Free groups
- Free abelian groups
- Presentations of groups
- Subgroups of free groups

### Textbooks

Possible textbooks for this course include (but are not limited to):