Topology 2: course

Book

Planned for Spring 2012.

Description

This is an introductory, one semester course on algebraic topology and its applications. It is intended for advanced undergraduate and beginning graduate students. It is dependent of point set topology.

Prerequisites

• sets, functions, etc,
• calculus (parts of),
• linear algebra and groups,
• proofs,
• Topology 1.

Lectures

The links below are outdated. The source of material is currently in a draft of a book called Topology Illustrated.

Introduction

• Topology: an introduction
• Quotient sets, the key construction
• Betti numbers
• Euler characteristic

Complexes

• Cell complexes
• Boundary operator
• New complexes from old:
  • subcomplexes
  • products of complexes
  • quotients of complexes

Fundamental group

• Loops
• Homotopy of loops
• Fundamental group
• Degree of map

Further reading

• Bredon, Geometry and Topology.
• Hatcher, Algebraic Topology.
• Related: Introduction to differential forms: course.