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Diff — Fiber bundle

Revision #1216 → #1827 · back to history

addedTangent bundle68192e03bdb5
addedGysin sequence96e519b3b17e
addedSections form a sheafec1daf3c1faa
modifiedG-atlascc5073d800f5
FieldFrom #1216To #1827
anchors[{"section":"Structure groups and transition functions","snippet":"atlas for the bundle"},{"type":"math_alttext","value":"{\\displaystyle \\varphi _{i}\\varphi _{j}^{-1}:\\left(U_{i}\\cap U_{j}\\right)\\times F\\to \\left(U_{i}\\cap U_{j}\\right)\\times F}"},{"type":"math_alttext","value":"{\\displaystyle \\varphi _{i}\\varphi _{j}^{-1}(x,\\,\\xi )=\\left(x,\\,t_{ij}(x)\\xi \\right)}"}]
modifiedG-bundle and structure group0ff481399e7a
FieldFrom #1216To #1827
anchors[{"section":"Structure groups and transition functions","snippet":"A G -bundle is a fiber bundle with an equivalence class of G -atlases"},{"type":"math_alttext","value":"{\\displaystyle \\varphi _{i}\\varphi _{j}^{-1}:\\left(U_{i}\\cap U_{j}\\right)\\times F\\to \\left(U_{i}\\cap U_{j}\\right)\\times F}"},{"type":"math_alttext","value":"{\\displaystyle \\varphi _{i}\\varphi _{j}^{-1}(x,\\,\\xi )=\\left(x,\\,t_{ij}(x)\\xi \\right)}"}]
modifiedBundle map / morphismea3ed6ef9ec0
FieldFrom #1216To #1827
anchors[{"section":"Bundle maps","snippet":"A bundle map or bundle morphism consists of a pair of continuous"},{"type":"math_alttext","value":"{\\displaystyle \\varphi :E\\to F,\\quad f:M\\to N}"}]