Controls
Čech Homology (approx.)
H₀ (components):–
H₁ (loops):–
Vertices |V|:–
Edges |E|:–
Triangles |T|:–
χ = V-E+T:–
The nerve of a cover {U_α} has:
• Vertex per set U_α
• Edge if U_α ∩ U_β ≠ ∅
• Triangle if U_α ∩ U_β ∩ U_γ ≠ ∅
Nerve theorem: If cover is good (all intersections contractible), nerve ≃ union of sets.
Vary r to see topology change at critical radii.
• Vertex per set U_α
• Edge if U_α ∩ U_β ≠ ∅
• Triangle if U_α ∩ U_β ∩ U_γ ≠ ∅
Nerve theorem: If cover is good (all intersections contractible), nerve ≃ union of sets.
Vary r to see topology change at critical radii.