Fixed point and duality theorems in algebraic topology

Contents: Roughly the contents are the following:

• Introduction.
• Manifolds and orientation. Definitions and local homological properties.
• Cap product, statements of Poincare duality for compact and non-compact manifolds.
• Proof of the Poincare duality theorem.
• Lefschetz and Alexander duality theorem: statements and proofs.
• Examples and applications of the duality theorems.
• Lefschetz fixed point theorem, its proof and applications.
• Exercises.

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