Overlap meridians recover the attaching loops: 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("The fundamental group of the circle"):::fully_proved
n1["Every abstract cell attachment has an indexed cone model"]:::fully_proved
n2["The auxiliary cover basepoint transports to the original basepoint"]:::fully_proved
n3["Each overlap piece has the homotopy type of its attaching sphere"]:::fully_proved
n4["The boundary of the two-disk is the circle"]:::fully_proved
n5("Overlap meridians recover the attaching loops"):::fully_proved
n6["Attaching 2-cells adds the attaching relations"]:::fully_proved
n0 --> n6
n0 -.-> n5
n0 --> n4
n1 --> n5
n2 --> n6
n2 --> n5
n5 --> n6
n3 --> n5
n4 --> n6
n4 --> n5
click n0 "../../../../../../roadmap/fundamental-group/basic-constructions/index.html#fundamental-group-circle" "The fundamental group of the circle — 1 item · 1 fully proved"
click n1 "../../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#abstract-cell-attachment-indexed-model" "Every abstract cell attachment has an indexed cone model — 1 item · 1 fully proved"
click n2 "../../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/auxiliary/index.html#auxiliary-cover-basepoint-transport" "The auxiliary cover basepoint transports to the original basepoint — 1 item · 1 fully proved"
click n3 "../../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/auxiliary/index.html#auxiliary-overlap-piece-sphere" "Each overlap piece has the homotopy type of its attaching sphere — 1 item · 1 fully proved"
click n4 "../../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#disk-boundary-two-circle" "The boundary of the two-disk is the circle — 1 item · 1 fully proved"
class n5 focus
click n5 "../../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/auxiliary/index.html#auxiliary-overlap-attaching-map" "Overlap meridians recover the attaching loops — 1 item · 1 fully proved"
click n6 "../../../../../../roadmap/fundamental-group/van-kampen/index.html#attach-two-cells-fundamental-group" "Attaching 2-cells adds the attaching relations — 1 item · 1 fully proved"