Turn geometric questions into algebraic ones through 21 interactive demonstrations.
See also: Topology for the foundational continuity and homeomorphism theory these invariants refine, Topological Data Analysis for persistent homology applied to high-dimensional point clouds, and Category Theory for the functors that turn topology into algebra.
Simplicial complexes, CW complexes, and the Euler characteristic
Chain complexes, boundary maps, and the key identity ∂² = 0
Detecting holes algebraically — cycles modulo boundaries
Dual invariants, the cup product, and cohomology rings
Unwrapping spaces, path lifting, and the Galois correspondence
Higher homotopy groups, the Hopf fibration, and exact sequences
Persistent homology, topological data analysis, and the grand timeline