The cyclic presentation complex: 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 proved7Proved, and every prerequisite is fully proved too.

graph LR n0("An indexed family of cones has a two-set open cover"):::fully_proved n1["An indexed cone attachment is a standard cell attachment"]:::fully_proved n2["The boundary of the two-disk is the circle"]:::fully_proved n3["Attaching 2-cells adds the attaching relations"]:::fully_proved n4("The degree-n circle map sends the generator to the degree-n loop"):::fully_proved n5["The degree-n circle relation gives the cyclic group"]:::fully_proved n6["The cyclic presentation complex"]:::fully_proved n3 --> n6 n4 --> n6 n5 --> n6 n2 --> n3 n2 --> n6 n1 --> n6 n0 --> n6 click n0 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#indexed-cone-open-cover" "An indexed family of cones has a two-set open cover — 1 item · 1 fully proved" click n1 "../../../../../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 n2 "../../../../../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 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/cell-attachment-support/index.html#circle-degree-map" "The degree-n circle map sends the generator to the degree-n loop — 1 item · 1 fully proved" click n5 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#cyclic-relation-quotient" "The degree-n circle relation gives the cyclic group — 1 item · 1 fully proved" class n6 focus click n6 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#cyclic-presentation-complex" "The cyclic presentation complex — 1 item · 1 fully proved"