Finite skeleta above dimension two have the same fundamental group: 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. fully proved6Proved, and every prerequisite is fully proved too.
graph LR
n0["Classical skeleton inclusions are abstract cell attachments"]:::fully_proved
n1["Attaching higher cells preserves the fundamental group"]:::fully_proved
n2("Higher-cell attachments preserve path components"):::fully_proved
n3("The 2-skeleton of a path-connected CW complex is path-connected"):::fully_proved
n4["Finite skeleta above dimension two have the same fundamental group"]:::fully_proved
n5["The 2-skeleton determines the fundamental group"]:::fully_proved
n0 -.-> n3
n0 -.-> n4
n1 -.-> n4
n2 -.-> n3
n2 -.-> n4
n3 -.-> n4
n4 -.-> n5
click n0 "../../../../roadmap/appendix/index.html#classical-skeleton-cell-attachment" "Classical skeleton inclusions are abstract cell attachments — 1 item · 1 fully proved"
click n1 "../../../../roadmap/fundamental-group/van-kampen/index.html#attach-higher-cells-fundamental-group" "Attaching higher cells preserves the fundamental group — 1 item · 1 fully proved"
click n2 "../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#higher-cell-attachment-path-components" "Higher-cell attachments preserve path components — 1 item · 1 fully proved"
click n3 "../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#path-connected-two-skeleton" "The 2-skeleton of a path-connected CW complex is path-connected — 1 item · 1 fully proved"
class n4 focus
click n4 "../../../../roadmap/fundamental-group/van-kampen/index.html#finite-skeleton-fundamental-group" "Finite skeleta above dimension two have the same fundamental group — 1 item · 1 fully proved"
click n5 "../../../../roadmap/fundamental-group/van-kampen/index.html#two-skeleton-fundamental-group" "The 2-skeleton determines the fundamental group — 1 item · 1 fully proved"