Geometry and topology

Master 1 lecture, first semester 2023-24

• Lectures: Christian Ausoni, Office D403, E-mail: ausoni (at) math.univ-paris13.fr
  
  
• Exercises: Gabriel Angelini-Knoll, office D403, E-mail: angelini-knoll (at) math.univ-paris13.fr
  
  

Lecture notes

• Chapter 1: Constructions of topological spaces (PDF-3.6M).
  
  
• Chapter 2: Topological manifolds (PDF-2.9M).
  
  
• Chapter 3: The fundamental group (PDF-5.1M).
  
  
• Chapter 4: The fundamental group of closed surfaces. (PDF-1.4M).
  
  

Exercise sheets

• Sheet 1 (PDF). To turn in: 1.5, 1.6.b, 1.7, 1.8.
  
  
• Sheet 2 (PDF). To turn in: 2.3, 2.6, 2.7.b, 2.9.
  
  
• Sheet 3 (PDF). To turn in: 3.6, 3.7.
  
  
• Sheet 4 (PDF). To turn in: 4.2, 4.3, 4.6.
  
  
• Sheet 5 (PDF). To turn in: 5.1, 5.6.
  
  
• Sheet 6 (PDF). To turn in: 6.2, 6.3, 6.6.
  
  
• Sheet 7 (PDF).
  
  
• Sheet 8 (PDF).
  
  

Literature

• J. M. Lee, Introduction to topological manifolds, New York, NY: Springer (2000).
  
  
• J. R. Munkres, Topology, 2nd ed. Upper Saddle River, NJ: Prentice Hall (2000).
  
  
• Allan Hatcher, Algebraic Topology, Cambridge University Press, 2002.
  Available from the author's webpage.
  
  
• Y. Félix and D. Tanré, Topologie algébrique, Cours et exercices corrigés. Master. CAPES/Agreg. Paris: Dunod (2010).