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:
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Representing homology classes by submanifolds and the genus function.
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Cobordisms and basic topological invariants.
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Intersection form of a 4-manifold and classification results.
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Examples of non-smoothable 4-manifolds.
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Elliptic complex surfaces: fiber sums and logarithmic transformations.
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Embeddings of surfaces in 4-manifolds.
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Knot traces and exotic smooth structures on R^4
- Bibiography:
- Hirsch, Differential topology.
- Gompf-Stipsicz, 4-manifolds and Kirby calculus
- Kirby, The topology of 4-manifolds.
Research Group: