Homotopic maps of pairs induce the same relative-homology map: 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 mathlib1Upstreamed into Mathlib.fully proved4Proved, and every prerequisite is fully proved too.

graph LR n0["Relative singular chains and homology"]:::fully_proved n1("Chain-homotopic maps induce the same homology map"):::mathlib n2["A homotopy of pairs gives a relative chain homotopy"]:::fully_proved n3("Homotopic maps of pairs induce the same relative-homology map"):::fully_proved n4("The identity simplex generates relative simplex homology"):::fully_proved n1 -.-> n3 n3 -.-> n4 n2 -.-> n3 n0 --> n3 n0 --> n2 click n0 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#relative-singular-homology" "Relative singular chains and homology — 1 item · 1 fully proved" click n1 "../../../../../roadmap/homology/simplicial-and-singular/index.html#chain-homotopy-invariance" "Chain-homotopic maps induce the same homology map — 1 item · 1 in mathlib" click n2 "../../../../../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" class n3 focus click n3 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#relative-homology-homotopy-invariance" "Homotopic maps of pairs induce the same relative-homology map — 1 item · 1 fully proved" click n4 "../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#relative-simplex-fundamental-class" "The identity simplex generates relative simplex homology — 1 item · 1 fully proved"