iv Contents
§2.5. Homeomorphisms 25
§2.6. Compactness 26
§2.7. Surfaces 27
§2.8. Manifolds 28
Chapter 3. The Gluing Construction 31
§3.1. Gluing Spaces Together 31
§3.2. The Gluing Construction in Action 33
§3.3. The Classification of Surfaces 36
§3.4. The Euler Characteristic 37
Chapter 4. The Fundamental Group 43
§4.1. A Primer on Groups 43
§4.2. Homotopy Equivalence 45
§4.3. The Fundamental Group 46
§4.4. Changing the Basepoint 48
§4.5. Functoriality 49
§4.6. Some First Steps 51
Chapter 5. Examples of Fundamental Groups 53
§5.1. The Winding Number 53
§5.2. The Circle 56
§5.3. The Fundamental Theorem of Algebra 57
§5.4. The Torus 58
§5.5. The 2-Sphere 58
§5.6. The Projective Plane 59
§5.7. A Lens Space 59
§5.8. The Poincar´ e Homology Sphere 62
Chapter 6. Covering Spaces and the Deck Group 65
§6.1. Covering Spaces 65
§6.2. The Deck Group 66
§6.3. A Flat Torus 67
Previous Page Next Page