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Algebraic and Geometric Topology. Part 1
1  Extension and lifting problems

1.1  The language of homotopy theory
1.2  The identity map extension problem
1.3  The identity map lifting problem

2  Fundamental groups and coverings

2.1  Paths, loops, and the fundamental group
2.2  Coverings and their automorphism groups
2.3  Cayley graphs and complexes

3  Manifolds and Lie groups

3.1  Spheres and projective spaces
3.3  Classical matrix groups
3.3  Spheres as H-spaces

4  Low dimensional manifolds

4.1  Classification of 1-manifolds
4.2  Classification of 2-manifolds
4.3  The Poincare 3-sphere

5  Knots, links, and braids

5.1  The genus of a knot
5.2  The linking number
5.3  The braid groups

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Algebraic and Geometric Topology. Part 2

1  Homology and cohomology groups

1.1  Homology groups – singular and cellular
1.2  Cohomology groups and rings
1.3  Poincare duality for manifolds

2  Homotopy groups and fibrations

2.1  The Hurewicz theorem
2.2  The Whitehead theorem
2.3  The exact sequence of fibration

3  Homotopy theory

2.1  Aspherical CW complexes
2.1  Eilenberg-McLane spaces
2.3  Postnikov systems

4  Four and higher dimensional manifolds

3.1  Simply connected four manifolds
3.2  Fundamental groups of homology spheres
3.3  The h-cobordism and s-cobordism theorems

5  Smooth manifolds and vector fields

5.1  Intersection numbers and transversality
5.2  Lefschetz fixed point theory
5.3  The Poincare-Hopf Theorem

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Algebraic and Geometric Topology. Part 3

1. Vector bundles

2. Characteristic classes

3. Topological K-theory

4. Cobordism theory

5. Manifolds and modular forms
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