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Topology Illustrated

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Topology Illustrated by Peter Saveliev

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The full text of the ongoing draft is below. The book is about homology.

Note: Simply click Back when you are finished and continue to the next section.


CONTENTS


Preface 1

Chapter 1. Cycles and boundaries

  1. Topology around us 13
  2. Homology classes 15
  3. Topology of graphs 13
  4. Homology groups of graphs 17
  5. Maps of graphs 19

Chapter 2. Topologies

  1. The intrinsic definition of continuity 11
  2. Neighborhoods and topologies 13
  3. Topological spaces 15
  4. Continuous functions 24
  5. Subspaces 20

Chapter 3. Complexes

  1. The binary algebra of cells 21
  2. Cubical complexes 19
  3. The algebra of oriented cells 19
  4. Simplicial complexes 21
  5. Simplicial homology 19
  6. Simplicial maps 24
  7. Parametric complexes 21

Chapter 4. Spaces

  1. Compact spaces 12
  2. Quotients 20
  3. Cell complexes 22
  4. Triangulations 19
  5. Manifolds 29
  6. Products 28

Chapter 5. Maps

  1. Homotopy 27
  2. Cell maps 25
  3. Maps of polyhedra 23
  4. Euler and Lefschetz numbers 16
  5. Set-valued maps 16
  6. Differential forms


Appendix: Student's guide to proof writing 3

Appendix: Notation 4


Estimated:

  • 555 pages
  • 716 illustrations
  • 717 exercises


References

These are the books I've used for teaching in the past: