The presentation complex has the presented 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["Attaching 2-cells adds the attaching relations"]:::fully_proved
n1["The fundamental group of a wedge of circles"]:::fully_proved
n2["Free-group relators form a standard two-cell attachment"]:::fully_proved
n3["Pointed wedges of path-connected spaces are path-connected"]:::fully_proved
n4["The presentation complex has the presented fundamental group"]:::fully_proved
n5("Presented groups have two-dimensional presentation complexes"):::fully_proved
n0 --> n4
n0 --> n2
n3 --> n4
n4 -.-> n5
n2 --> n4
n1 --> n4
n1 --> n2
click n0 "../../../../../roadmap/fundamental-group/van-kampen/index.html#attach-two-cells-fundamental-group" "Attaching 2-cells adds the attaching relations — 1 item · 1 fully proved"
click n1 "../../../../../roadmap/fundamental-group/van-kampen/index.html#wedge-circles-free-group" "The fundamental group of a wedge of circles — 1 item · 1 fully proved"
click n2 "../../../../../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 n3 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#pointed-wedge-path-connected" "Pointed wedges of path-connected spaces are path-connected — 1 item · 1 fully proved"
class n4 focus
click n4 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#presentation-complex-fundamental-group" "The presentation complex has the presented fundamental group — 1 item · 1 fully proved"
click n5 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#presentation-complex-realization" "Presented groups have two-dimensional presentation complexes — 1 item · 1 fully proved"