Difference between revisions of "Xypic/Fibration"

Latest revision as of 14:52, 11 May 2015

[math] \begin{xy} %vertices (27,0)*+{E^{[0]}=B}="v1";(0,20)*+{E^{[1]}}="v2";(70,20)*+{F^{[1]}}="v3";% (25,35)*+{K\left(\pi_1(F),1\right)}="v4";% (95,35)*+{K\left(\pi_1(F),1\right)}="v5";% (0,45)*+{\vdots}="v6";(70,45)*+{\vdots}="v7";(0,70)*+{E^{[n-1]}}="v8";% (70,70)*+{F^{[n-1]}}="v9";(25,85)*+{K\left(\pi_{n-1}(F),n-1\right)}="v10";% (95,85)*+{K\left(\pi_{n-1}(F),n-1\right)}="v11";(-20,100)*+{E}="v12";% (50,100)*+{F}="v13";(0,115)*+{E^{[n]}}="v14";(70,115)*+{F^{[n]}}="v15";% (25,130)*+{K\left(\pi_{n}(F),n\right)}="v16";% (95,130)*+{K\left(\pi_{n}(F),n\right)}="v17"; (0,150)*+{\vdots}="v18";(70,150)*+{\vdots}="v19"; {\ar@{->>}^{p_{n+1}} "v18"; "v14"};{\ar@{->>} "v19"; "v15"};% {\ar@{^{(}->} "v16";"v14" };{\ar@{^{(}->} "v17";"v15" };% {\ar@{_{(}->} "v15";"v14" };% {\ar@{->}^{h_{n}} "v12"; "v14"};{\ar@{->}^{h’_{n}} "v13"; "v15"};% {\ar@{_{(}->} "v13";"v12" }; {\ar@{->>}^{p_{n}}|(.33){\hole} "v14"; "v8"};% {\ar@{->}^{h_{n-1}} "v12"; "v8"};{\ar@{->}^{h_{1}} "v12"; "v2"};% {\ar@{->>} "v15"; "v9"};% {\ar@{->}^{h’_{n-1}} "v13"; "v9"};{\ar@{->}_{h’_{1}} "v13"; "v3"};% {\ar@{_{(}->} |(.18){\hole} "v9";"v8" };% {\ar@{^{(}->} "v10";"v8" };% {\ar@{^{(}->} "v11";"v9" }; {\ar@{->>} "v8"; "v6"};{\ar@{->>} "v9"; "v7"};% {\ar@{->>} "v6"; "v2"};{\ar@{->>} "v7"; "v3"};% {\ar@{^{(}->}|(.35){\hole} "v4";"v2" };% {\ar@{^{(}->} "v5";"v3" }; {\ar@{->}"v8"; "v1"};% {\ar@{_{(}->}|(.725){\hole} "v3";"v2" }; {\ar@{->>}_{q_1=p_1}"v2"; "v1"};% \end{xy} [/math]