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• Tags
  • #geomtop
• Refs:
  • Classification of 4-manifolds #resources/videos
  • Stanford course notes: https://stanford.edu/~sfh/283A.pdf#page=2 #resources/course-notes
• Links:
  • Unsorted/Rohklin’s theorem
  • Unsorted/Kodaira-Spencer
  • Unsorted/riemannian manifold
  • Unsorted/intersection form
  • Unsorted/Rokhlin theorem

4-Manifolds

There exist (simply connected) closed oriented 4-manifolds which are homeomorphic but not diffeomorphic

Review Terms

#projects/review #projects/notes/reading #todo/questions

• What is the tautological bundle?
• What is Serre duality?
• What is Hirzebruch-Riemann-Roch?
• How is \(\mathcal{O}(n)\) defined?
• What is a Kahler manifold?
• What is \(A^{p, q}\)?
• How is Dolbeaut cohomology defined?
• What is Noether’s formula?
• What is the symbol of an operator?
• What is an elliptic complex?
• What is the Aatiyah-Singer Index Theorem?
• What is the Chern class?
• What is the Chern character?
• What are Chern roots?
• What is the Todd class?
• What is the Euler class?
• What is the Laplacian?
• What is a Hermitian metric?
• What is the Hodge star?
• What is the genus formula?
• What is the blowup
  • What is the exceptional divisor?
  • What is the strict transform?
  • What is the blowdown
• What is a unimodular lattice?
• What is the Steifel-Whitney class?
• What is the Pontrayagin class?
• What is a Kahler?
• What is a spin?
• What is the Clifford algebra?
• What is the Dirac equation

Useful techniques: fiber sum and rational blowdown