Free-group relators form a standard two-cell attachment: 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["An indexed cone attachment is a standard cell attachment"]:::fully_proved
n1["Attaching 2-cells adds the attaching relations"]:::fully_proved
n2["Every fundamental-group element has a based disk-boundary representative"]:::fully_proved
n3["The fundamental group of a wedge of circles"]:::fully_proved
n4["Free-group relators form a standard two-cell attachment"]:::fully_proved
n5["The presentation complex has the presented fundamental group"]:::fully_proved
n6["The presentation complex is an abstract two-dimensional CW complex"]:::fully_proved
n1 --> n5
n1 --> n4
n0 --> n4
n2 --> n4
n4 --> n6
n4 --> n5
n3 --> n5
n3 --> n4
click n0 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#indexed-basic-cell-attachment" "An indexed cone attachment is a standard cell attachment — 1 item · 1 fully proved"
click n1 "../../../../../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 n2 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#disk-boundary-fundamental-group-representative" "Every fundamental-group element has a based disk-boundary representative — 1 item · 1 fully proved"
click n3 "../../../../../roadmap/fundamental-group/van-kampen/index.html#wedge-circles-free-group" "The fundamental group of a wedge of circles — 1 item · 1 fully proved"
class n4 focus
click n4 "../../../../../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 n5 "../../../../../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 n6 "../../../../../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"