Geometry of Fibre Bundle （课程）
主讲人： 王宏玉 教授 （扬州大学数学系）
时间： 每周二 下午 13：00
地点： 闵行数学系 130
内容： 预修 diff. mfld..
Ch.1. Fibre Bundles
1. The def. of vector bundle
2. Construction of new vector bundles
3. Metric and orientation
4. Holomorphic vector bundle
5. G-space and principal G-bundles
6. Associated bundle
Ch.2 Classification of bundles
1. Classification of bundles and Cech cohomology
2. Homotopy equivalent lemma
3. Classifying spaces
4. Remarks
Ch.3 Connections and curvatures
1. The conn. on the principal bundles
2. Parallel displacement, holonomy groups and flat connections
3. Curvature form on principal bundles
4. Connections and curvatures vector bundles
Ch.4 Characteristic classes
1. Chern classes
2. The compatation of Chern classes
Ch.5 Gange group
1. Gange transformations
2. Sobolev spaces