Knot Theory Manifolds Algebraic Topology Shape and Structure Geometric Operations Surgery 4-Manifolds Topological Invariants Hodge Structures Homology Limit Points Surface Links Geometric Properties Trivial Components Aspheric Components Proofs Fractal Geometry Energy Topology Homeomorphism Disk Topology Etale Cohomology Global Analysis Mathematical Properties of Topology Persistent Homology Quotient Spaces Material Properties