Presentation-complex support dependency map
This map shows the container's direct articles. Nested containers are collapsed and clickable; dependency edges are rolled up from their leaves. fully proved25Proved, and every prerequisite is fully proved too.
graph LR
n0["Collapsing the boundary of a one-disk gives the circle"]:::fully_proved
n1["The cyclic presentation complex"]:::fully_proved
n2["Every fundamental-group element has a based disk-boundary representative"]:::fully_proved
n3["The identity attaches an empty family of cells"]:::fully_proved
n4["Eventually constant cell sequences form abstract CW complexes"]:::fully_proved
n5["A point is one standard zero-cell"]:::fully_proved
n6["Pointed wedges of path-connected spaces are path-connected"]:::fully_proved
n7["Continuous maps out of a pointed wedge"]:::fully_proved
n8["The presentation complex is an abstract two-dimensional CW complex"]:::fully_proved
n9["The presentation complex has the presented fundamental group"]:::fully_proved
n10("Presented groups have two-dimensional presentation complexes"):::fully_proved
n11["Free-group relators form a standard two-cell attachment"]:::fully_proved
n12["A wedge of circles is an indexed one-cell attachment"]:::fully_proved
n13["External chapter: The fundamental group<br/><small>11 items · 11 fully proved</small>"]:::boundary
n14["External chapter: Homology<br/><small>1 item · 1 fully proved</small>"]:::boundary
n13 -->|2| n0
n13 -->|6| n1
n13 --> n2
n13 --> n5
n13 --> n6
n13 --> n7
n13 -->|2| n9
n13 -->|3| n11
n13 -->|2| n12
n0 --> n12
n2 --> n11
n3 --> n8
n4 --> n8
n5 --> n8
n6 --> n9
n7 -.-> n14
n7 --> n12
n8 -.-> n10
n9 -.-> n10
n10 -.-> n13
n11 --> n8
n11 --> n9
n12 --> n8
click n0 "../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#circle-one-cell-quotient" "Collapsing the boundary of a one-disk gives the circle — 1 item · 1 fully proved"
click n1 "../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#cyclic-presentation-complex" "The cyclic presentation complex — 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/presentation-complex/index.html#empty-cell-attachment-constructor" "The identity attaches an empty family of cells — 1 item · 1 fully proved"
click n4 "../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#eventually-constant-cell-sequence" "Eventually constant cell sequences form abstract CW complexes — 1 item · 1 fully proved"
click n5 "../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#point-zero-cell-attachment" "A point is one standard zero-cell — 1 item · 1 fully proved"
click n6 "../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#pointed-wedge-path-connected" "Pointed wedges of path-connected spaces are path-connected — 1 item · 1 fully proved"
click n7 "../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#pointed-wedge-universal-property" "Continuous maps out of a pointed wedge — 1 item · 1 fully proved"
click n8 "../../../../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"
click n9 "../../../../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 n10 "../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#presentation-complex-realization" "Presented groups have two-dimensional presentation complexes — 1 item · 1 fully proved"
click n11 "../../../../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 n12 "../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#wedge-circles-one-skeleton" "A wedge of circles is an indexed one-cell attachment — 1 item · 1 fully proved"
click n13 "../../../chapters/fundamental-group.html" "The fundamental group — 11 items · 11 fully proved"
click n14 "../../../chapters/homology.html" "Homology — 1 item · 1 fully proved"