A topological homotopy gives a singular-chain homotopy: 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. What the colours mean

in mathlib3Upstreamed into Mathlib.fully proved2Proved, and every prerequisite is fully proved too.

graph LR n0["The singular chain complex"]:::mathlib n1["A topological homotopy gives a singular-chain homotopy"]:::mathlib n2("Homotopic maps induce the same singular-homology map"):::mathlib n3["A homotopy of pairs gives a relative chain homotopy"]:::fully_proved n4("Homotopic maps induce the same reduced-homology map"):::fully_proved n0 --> n2 n0 --> n1 n1 -.-> n4 n1 -.-> n3 n1 -.-> n2 click n0 "../../../../roadmap/homology/simplicial-and-singular/index.html#singular-chain-complex" "The singular chain complex — 1 item · 1 in mathlib" class n1 focus click n1 "../../../../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 n2 "../../../../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 n3 "../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#relative-singular-chain-homotopy" "A homotopy of pairs gives a relative chain homotopy — 1 item · 1 fully proved" click n4 "../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#reduced-homology-homotopy-invariance" "Homotopic maps induce the same reduced-homology map — 1 item · 1 fully proved"