The presentation complex is an abstract two-dimensional CW complex: 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 proved7Proved, and every prerequisite is fully proved too.
graph LR
n0["Free-group relators form a standard two-cell attachment"]:::fully_proved
n1["A point is one standard zero-cell"]:::fully_proved
n2["A wedge of circles is an indexed one-cell attachment"]:::fully_proved
n3["The identity attaches an empty family of cells"]:::fully_proved
n4["Eventually constant cell sequences form abstract CW complexes"]:::fully_proved
n5["The presentation complex is an abstract two-dimensional CW complex"]:::fully_proved
n6("Presented groups have two-dimensional presentation complexes"):::fully_proved
n3 --> n5
n4 --> n5
n1 --> n5
n5 -.-> n6
n0 --> n5
n2 --> n5
click n0 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#relator-cell-attachment" "Free-group relators form a standard two-cell attachment — 1 item · 1 fully proved"
click n1 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#point-zero-cell-attachment" "A point is one standard zero-cell — 1 item · 1 fully proved"
click n2 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#wedge-circles-one-skeleton" "A wedge of circles is an indexed one-cell attachment — 1 item · 1 fully proved"
click n3 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#empty-cell-attachment-constructor" "The identity attaches an empty family of cells — 1 item · 1 fully proved"
click n4 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#eventually-constant-cell-sequence" "Eventually constant cell sequences form abstract CW complexes — 1 item · 1 fully proved"
class n5 focus
click n5 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#presentation-complex-cw-structure" "The presentation complex is an abstract two-dimensional CW complex — 1 item · 1 fully proved"
click n6 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#presentation-complex-realization" "Presented groups have two-dimensional presentation complexes — 1 item · 1 fully proved"