The boundary of the two-disk is the circle: 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. What the colours mean

fully proved6Proved, and every prerequisite is fully proved too.

graph LR n0("The fundamental group of the circle"):::fully_proved n1["The boundary of the two-disk is the circle"]:::fully_proved n2("Overlap meridians recover the attaching loops"):::fully_proved n3["Attaching 2-cells adds the attaching relations"]:::fully_proved n4["Every fundamental-group element has a based disk-boundary representative"]:::fully_proved n5["The cyclic presentation complex"]:::fully_proved n0 --> n3 n0 -.-> n2 n0 --> n1 n3 --> n5 n2 --> n3 n1 --> n3 n1 --> n2 n1 --> n5 n1 --> n4 click n0 "../../../../../roadmap/fundamental-group/basic-constructions/index.html#fundamental-group-circle" "The fundamental group of the circle — 1 item · 1 fully proved" class n1 focus click n1 "../../../../../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" click n2 "../../../../../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 n3 "../../../../../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 n4 "../../../../../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 n5 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#cyclic-presentation-complex" "The cyclic presentation complex — 1 item · 1 fully proved"