Chapter 1 Chapters 2 and 3
Midterm 2 topics

  • Topological properties
    • Connectedness
    • Compactness
    • Path-connectedness
  • Definiton of manifold
  • Definition of surface
  • Definition of surface with boundary
  • Connected sum construction
  • Plane models of surfaces
  • Orientability
  • Classification of surfaces
  • Cell complexes
  • Euler characteristic
  • Genus
Sample problems
Chapter 1
  1. 1.3.10
  2. 1.3.19
  3. 1.3.24
  4. 1.3.29
  5. 1.3.31
Chapters 2 and 3
  1. 2.2.7 (note the correction) Justify your answer (it is OK to justify with clear, relevant pictures
  2. 2.3.2
  3. 2.3.6
  4. 2.3.9
  5. 2.3.21
  6. 2.5.4.a
  7. 2.6.3
  8. 2.6.6
  9. 2.6.7
  10. 2.7.3
  11. 2.7.5
  12. 2.7.6
  13. 2.7.7
  14. 3.1.11
  15. 3.1.12
  16. 3.1.14
  17. 3.1.17
  18. 3.1.18
  19. 3.3.3
  20. Determine what surface is obtained by the connected sum of two Mobius bands.