The triple connecting map sends a relative cycle to its boundary: 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

fully proved4Proved, and every prerequisite is fully proved too.

graph LR n0("Relative chains of a triple form a short exact sequence"):::fully_proved n1("The long exact sequence of a triple"):::fully_proved n2("The triple connecting map sends a relative cycle to its boundary"):::fully_proved n3("The identity simplex generates relative simplex homology"):::fully_proved n2 -.-> n3 n0 --> n2 n0 --> n1 n1 -.-> n3 n1 -.-> n2 click n0 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#triple-chain-short-exact-sequence" "Relative chains of a triple form a short exact sequence — 1 item · 1 fully proved" click n1 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#triple-long-exact-sequence" "The long exact sequence of a triple — 1 item · 1 fully proved" class n2 focus click n2 "../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#triple-connecting-cycle-formula" "The triple connecting map sends a relative cycle to its boundary — 1 item · 1 fully proved" click n3 "../../../../../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"