Topology

  1. Advanced Topics
    1. Homotopy Type Theory
      1. Higher Category Theory
        1. Infinity Categories
          1. Model Categories
          2. Algebraic K-Theory
            1. K₀ and K₁ Groups
              1. Higher K-Groups
                1. Applications to Topology
                2. Characteristic Classes
                  1. Chern Classes
                    1. Stiefel-Whitney Classes
                      1. Pontryagin Classes
                        1. Applications to Vector Bundles
                        2. Spectral Sequences
                          1. Definition and Basic Properties
                            1. Serre Spectral Sequence
                              1. Adams Spectral Sequence
                                1. Applications to Homotopy Groups
                                2. Topology and Physics
                                  1. Topological Quantum Field Theory
                                    1. Chern-Simons Theory
                                      1. Topological Phases of Matter
                                        1. Applications in Condensed Matter
                                        2. Computational Topology
                                          1. Persistent Homology
                                            1. Topological Data Analysis
                                              1. Algorithms for Topological Invariants
                                                1. Applications in Data Science

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                                              5. Geometric Topology

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                                              1. Introduction to Topological Concepts