Topology
Higher Category Theory
Infinity Categories
Model Categories
K₀ and K₁ Groups
Higher K-Groups
Applications to Topology
Chern Classes
Stiefel-Whitney Classes
Pontryagin Classes
Applications to Vector Bundles
Definition and Basic Properties
Serre Spectral Sequence
Adams Spectral Sequence
Applications to Homotopy Groups
Topological Quantum Field Theory
Chern-Simons Theory
Topological Phases of Matter
Applications in Condensed Matter
Persistent Homology
Topological Data Analysis
Algorithms for Topological Invariants
Applications in Data Science
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5. Geometric Topology
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1. Introduction to Topological Concepts