Topology

  1. Geometric Topology
    1. Surfaces
      1. Classification of Surfaces
        1. Orientable Surfaces
          1. Non-Orientable Surfaces
            1. Connected Sum Operation
              1. Classification Theorem
              2. Fundamental Groups of Surfaces
                1. Presentations of Surface Groups
                  1. Genus and Fundamental Group
                  2. Mapping Class Groups
                    1. Diffeomorphisms of Surfaces
                      1. Dehn Twists
                        1. Generators and Relations
                        2. Riemann Surfaces
                          1. Complex Structure on Surfaces
                            1. Uniformization Theorem
                          2. Knot Theory
                            1. Reidemeister Moves
                              1. Three Types of Moves
                                1. Equivalence of Diagrams
                                2. Knot Invariants
                                  1. Linking Number
                                    1. Tricolorability
                                      1. Knot Group
                                        1. Alexander Polynomial
                                          1. Jones Polynomial
                                            1. HOMFLY Polynomial
                                            2. Knot Complements
                                              1. Topology of Complement
                                                1. Fundamental Group
                                                  1. Gordon-Luecke Theorem
                                                2. Three-Manifolds
                                                  1. Examples and Constructions
                                                    1. Lens Spaces
                                                      1. Seifert Fiber Spaces
                                                        1. Hyperbolic Manifolds
                                                        2. Heegaard Splittings
                                                          1. Handlebody Decompositions
                                                            1. Heegaard Genus
                                                            2. Prime Decomposition
                                                              1. Connected Sum
                                                                1. Prime and Composite Manifolds
                                                                  1. Uniqueness of Prime Decomposition
                                                                  2. Geometrization
                                                                    1. Thurston's Eight Geometries
                                                                      1. Geometrization Conjecture
                                                                        1. Perelman's Proof
                                                                        2. JSJ Decomposition
                                                                          1. Torus Decompositions
                                                                            1. Seifert Fibered Pieces
                                                                              1. Hyperbolic Pieces

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                                                                          4. Differential Topology

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                                                                          6. Advanced Topics