Topology Illustrated. Volume 2

Algebraic topology is the main subject of this book that initially follows a two-semester first course in topology. It furthermore takes the reader to more advanced parts of algebraic topology as well as some applications: the shape of the universe, configuration spaces, digital image analysis, data analysis, social choice, exchange economy. An overview of discrete calculus is also included. The book contains over 1000 color illustrations and over 1000 exercises.CONTENTSChapter 4. Spaces 1. Compacta 2. Quotients 3. Cell complexes 4. Triangulations 5. Manifolds 6. ProductsChapter 5. Maps 1. Homotopy 2. Cell maps 3. Maps of polyhedra 4. The Euler and Lefschetz numbers 5. Set-valued mapsChapter 6. Forms 1. Discrete forms and cochains 2. Calculus on cubical complexes 3. Cohomology 4. Metric tensorChapter 7. Flows 1. Metric complexes 2. ODEs 3. PDEs 4. Social choiceThis is a new edition, corrected and updated. I had to split the paper version into two volumes because of Amazon's page limits. There is no solution manual in the works at this time. Read more