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4-manifolds

Lecturer: 
Course Type: 
PhD Course
Academic Year: 
2024-2025
Period: 
October - January
Duration: 
20 h
Description: 
 The course is an introduction to 4-manifolds with a focus on the construction of inequivalent smooth structures.  It will be mostly example-driven with case studies related to algebraic and complex geometry. 
  • Topics:
  1. Representing homology classes by submanifolds and the genus function.
  2. Cobordisms and basic topological invariants.
  3. Intersection form of a 4-manifold and classification results.
  4. Examples of non-smoothable 4-manifolds.
  5. Elliptic complex surfaces: fiber sums and logarithmic transformations.
  6. Embeddings of surfaces in 4-manifolds.
  7. Knot traces and exotic smooth structures on R^4
  • Bibiography:
  1. Hirsch, Differential topology. 
  2. Gompf-Stipsicz, 4-manifolds and Kirby calculus
  3. Kirby, The topology of 4-manifolds.

 

 

Next Lectures: 
Tuesday, November 12, 2024 - 09:00 to 11:00
Thursday, November 14, 2024 - 11:00 to 13:00
Tuesday, November 19, 2024 - 09:00 to 11:00
Thursday, November 21, 2024 - 11:00 to 13:00
Tuesday, November 26, 2024 - 09:00 to 11:00
Thursday, November 28, 2024 - 11:00 to 13:00
Tuesday, December 3, 2024 - 09:00 to 11:00
Thursday, December 5, 2024 - 11:00 to 13:00
Tuesday, December 10, 2024 - 09:00 to 11:00
Thursday, December 12, 2024 - 11:00 to 13:00
Tuesday, December 17, 2024 - 09:00 to 11:00
Thursday, December 19, 2024 - 11:00 to 13:00

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