Index of notation and defined terms 2-sided, 32 A ⊗R B, 35 B(6), 64 C′( 1 n ), 77, 85 C(p), 85 C(p) small-cancellation condition, 82 H-wall, 71 N(H), 14 WProjX(B → A), 41 ∢(c), 81 ∂pD, 15 CG(H), 26 Hull(HK), 28 MQH, 107 VH-complex, 11 ⟨⟨H1,H2,...⟩⟩, 78 Nμ(H), 25 ∣∣Yi∣∣, 86 ∣P∣, 86 i-shell, 82 n-cube, 7 #(p,q), 14 ∁(Y → X), 36 Absorbing squares, 86 acts, 54 admit, 89 Admitted rectangles, 89 almost malnormal, 25 almost malnormal quasiconvex hierarchy, 107 alternating, 8 angle, 81 angled 2-complex, 81 annuladder, 103 annular diagram, 101 annular diagram in X∗, 101 axis, 67 B(6), 64 betwixts, 53 bicollared, 103 boundary cycle, 15 boundary path, 15 bounded packing, 62 cage, 128 cancelable pair, 84 canceled pair, 17 canonical 0-cube, 65 canonical completion, 36 canonical cube, 65 canonical retraction, 36 carrier, 14, 58, 98 CAT(0) cube complex, 8 cladder, 99 class, 103 clean, 12 codimension-1, 58 Combining cone-cells, 85 commensurable, 26 commensurator, 26 complete square complex, 11 cone-cell, 79 cone-piece, 89 consecutive, 98 convex, 14 convex wallspace, 96 core, 27 cornsquare, 21 cosparsely, 65 cross, 61 crossing graph, 33 cube complex, 7 cubical hierarchy, 126 cubical presentation, 78 curvature at a 2-cell, 81 cut-wall, 67 cutting along a hyperplane, 126 cyclic hierarchy, 132 139

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