Topology Illustrated. Volume 1

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.CONTENTS VOLUME 1Chapter 1. Cycles 1. Topology around us 2. Homology classes 3. Topology of graphs 4. Homology groups of graphs 5. Maps of graphs 6. Binary calculus on graphsChapter 2. Topologies 1. A new look at continuity 2. Neighborhoods and topologies 3. Topological spaces 4. Continuous functions 5. SubspacesChapter 3. Complexes 1. The algebra of cells 2. Cubical complexes 3. The algebra of oriented cells 4. Simplicial complexes 5. Simplicial homology 6. Simplicial maps 7. Parametric complexesThis 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