The binary-cover Mayer–Vietoris sequence: 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 mathlib1Upstreamed into Mathlib.fully proved5Proved, and every prerequisite is fully proved too.
graph LR
n0("A short exact sequence gives an exact homology sequence"):::mathlib
n1["Small singular chains include by a chain-homotopy equivalence"]:::fully_proved
n2("The binary-cover excision chain map is a homotopy equivalence"):::fully_proved
n3("Binary-cover chains form a short exact sequence"):::fully_proved
n4("The binary-cover Mayer–Vietoris sequence"):::fully_proved
n5("The ordinary neighborhood-retract Mayer–Vietoris sequence"):::fully_proved
n3 --> n4
n4 --> n5
n0 -.-> n4
n2 --> n4
n1 -.-> n4
n1 -.-> n2
click n0 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#short-exact-homology-sequence" "A short exact sequence gives an exact homology sequence — 1 item · 1 in mathlib"
click n1 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/small-chains-and-excision/index.html#small-chain-inclusion-homotopy-equivalence" "Small singular chains include by a chain-homotopy equivalence — 1 item · 1 fully proved"
click n2 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/small-chains-and-excision/index.html#binary-cover-excision-chain-equivalence" "The binary-cover excision chain map is a homotopy equivalence — 1 item · 1 fully proved"
click n3 "../../../../../roadmap/homology/computations-and-applications/mayer-vietoris/index.html#binary-cover-chain-short-exact-sequence" "Binary-cover chains form a short exact sequence — 1 item · 1 fully proved"
class n4 focus
click n4 "../../../../../roadmap/homology/computations-and-applications/mayer-vietoris/index.html#binary-cover-mayer-vietoris-sequence" "The binary-cover Mayer–Vietoris sequence — 1 item · 1 fully proved"
click n5 "../../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#ordinary-neighborhood-mayer-vietoris" "The ordinary neighborhood-retract Mayer–Vietoris sequence — 1 item · 1 fully proved"