The singular chain complex: local context
Project map · Chapter map · Full theorem DAG · Open textbook statement
This local map shows one dependency hop in either direction. The highlighted item is the current focus. in mathlib4Upstreamed into Mathlib.fully proved3Proved, and every prerequisite is fully proved too.
graph LR
n0["The singular chain complex"]:::mathlib
n1["Singular homology"]:::mathlib
n2["The augmented singular chain complex"]:::fully_proved
n3["A topological homotopy gives a singular-chain homotopy"]:::mathlib
n4("Homotopic maps induce the same singular-homology map"):::mathlib
n5["Singular-chain subdivision is naturally homotopic to the identity"]:::fully_proved
n6["The binary-cover Mayer–Vietoris chain complex"]:::fully_proved
n0 --> n6
n0 --> n2
n0 --> n5
n0 --> n1
n0 --> n4
n0 --> n3
n3 -.-> n4
class n0 focus
click n0 "../../../../roadmap/homology/simplicial-and-singular/index.html#singular-chain-complex" "The singular chain complex — 1 item · 1 in mathlib"
click n1 "../../../../roadmap/homology/simplicial-and-singular/index.html#singular-homology" "Singular homology — 1 item · 1 in mathlib"
click n2 "../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#augmented-singular-chain-complex" "The augmented singular chain complex — 1 item · 1 fully proved"
click n3 "../../../../roadmap/homology/simplicial-and-singular/index.html#topological-homotopy-chain-homotopy" "A topological homotopy gives a singular-chain homotopy — 1 item · 1 in mathlib"
click n4 "../../../../roadmap/homology/simplicial-and-singular/index.html#singular-homology-homotopy-invariance" "Homotopic maps induce the same singular-homology map — 1 item · 1 in mathlib"
click n5 "../../../../roadmap/homology/simplicial-and-singular/relative-homology/small-chains-and-excision/index.html#singular-chain-subdivision-homotopy" "Singular-chain subdivision is naturally homotopic to the identity — 1 item · 1 fully proved"
click n6 "../../../../roadmap/homology/computations-and-applications/mayer-vietoris/index.html#binary-cover-chain-complex" "The binary-cover Mayer–Vietoris chain complex — 1 item · 1 fully proved"