Each overlap piece has the homotopy type of its attaching sphere: 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 proved5Proved, and every prerequisite is fully proved too.
graph LR
n0("The auxiliary overlap has an indexed open cover"):::fully_proved
n1["The single-cone cover intersection has the homotopy type of its boundary"]:::fully_proved
n2["Each overlap piece has the homotopy type of its attaching sphere"]:::fully_proved
n3("An open-cover model for attached cells"):::fully_proved
n4("Overlap meridians recover the attaching loops"):::fully_proved
n0 -.-> n3
n0 --> n2
n2 -.-> n3
n2 --> n4
n1 -.-> n2
click n0 "../../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/auxiliary/index.html#auxiliary-overlap-open-cover" "The auxiliary overlap has an indexed open cover — 1 item · 1 fully proved"
click n1 "../../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#single-cone-intersection" "The single-cone cover intersection has the homotopy type of its boundary — 1 item · 1 fully proved"
class n2 focus
click n2 "../../../../../../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 n3 "../../../../../../roadmap/fundamental-group/van-kampen/index.html#cell-attachment-cover-model" "An open-cover model for attached cells — 1 item · 1 fully proved"
click n4 "../../../../../../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"