This site contains an **online textbook** as well as other mathematical content. Created and run by Peter Saveliev.

# Topology Illustrated

### From Intelligent Perception

(Redirected from Betti numbers)

*Topology Illustrated*-- full text of the ongoing draft --

**CONTENTS**

Preface 1

**Chapter 1. Cycles and boundaries**

- Topology around us 13
- Homology classes 15
- Topology of graphs 13
- Homology groups of graphs 17
- Maps of graphs 19
- Cochains on graphs 11

**Chapter 2. Topologies**

- The intrinsic definition of continuity 11
- Neighborhoods and topologies 13
- Topological spaces 15
- Continuous functions 24
- Subspaces 20

**Chapter 3. Complexes**

- The binary algebra of cells 21
- Cubical complexes 19
- The algebra of oriented cells 19
- Simplicial complexes 21
- Simplicial homology 19
- Simplicial maps 24
- Parametric complexes 21

**Chapter 4. Spaces**

- Compacta 12
- Quotients 20
- Cell complexes 22
- Triangulations 19
- Manifolds 29
- Products 28

**Chapter 5. Maps**

**Chapter 6. Differential forms**

- Discrete forms as cochains 24
- How to get started with discrete calculus 20
- Cohomology 22
- Multilinear algebra 14
- Geometries 26
- Diffusion 17

- Appendix: Student's guide to proof writing 3
- Appendix: Notation 4
- Appendix: Discrete calculus with Excel 6

Estimated:

- 698 pages
- 873 illustrations
- 846 exercises