This site contains: mathematics courses and book; covers: image analysis, data analysis, and discrete modelling; provides: image analysis software. Created and run by Peter Saveliev.

From Intelligent Perception

Planned for Spring 2012.

1 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.

2 Prerequisites

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

3 Lectures

The lectures now are a part of a draft of a book called Applied Topology and Geometry.

3.1 Introduction

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

3.2 Complexes

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

3.3 Fundamental group

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

4 Notes

5 Further reading

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