Introduction to Geometric Topology

Abstract

This is an introductory course in algebraic topology with an emphasis on a geometric point of view. The course will focus on the fundamental group, ways to compute it, and applications to topology, group theory, and complex analysis.

Syllabus

Homotopy, the fundamental group, covering spaces, methods to compute the fundamental group, free groups, the Seifert-van Kampen theorem, applications to geometry, topology, group theory and complex analysis, invariants of knots, introduction to homotopy theory.

Prerequisites

• General topology
• Complex analysis (functions of one complex variable)
• Algebra I (basic knowledge of the concept of group)

Recommended books and reading materials

• G. Bredon: "Topology and geometry". Graduate Texts in Mathematics, 139. Springer-Verlag.
• A. Hatcher: "Algebraic topology". Cambridge University Press. You can download the entire book from Hatcher's webpage. You can find on that webpage many other interesting books and texts.