1. Root Space Decompositions 2 2. Weights 5 3. Weyl Group 8 4. Irreducible Representations 11 5. Basic Concepts of Vector Bundles 13 6. Line Bundles 17 7. Curvature 20 7.1. Curvature of tangent bundles 22 7.2. Curvature of line bundles 24 7.3. Levi curvature 25 8. Ampleness Formulas 27 8.1. Ampleness of irreducible bundles 28 8.2. Ampleness of tangent bundles 29 9. Chern Classes 32 9.1. Chern c...

Introduction 1 1. Bundles 2 1.1. Pullback 2 1.2. Sections 3 1.3. Fiber bundles as fibrations 4 2. Vector bundles 4 2.1. Whitney sum 5 2.2. Sections of vector bundles 6 2.3. Inner products 6 3. Principal Bundles 7 3.1. Morphisms 7 3.2. Sections and trivializations 8 3.3. Associated bundles 9 3.4. Homotopy classification 11 3.5. B as a functor 14 4. Characteristic classes 16 4.1. Line Bundles 16 ...

In developing Drosophila bristles two species of cross-linker, the forked proteins and fascin, connect adjacent actin filaments into bundles. Bundles form in three phases: (a) tiny bundles appear; (b) these bundles aggregate into larger bundles; and (c) the filaments become maximally cross-linked by fascin. In mutants that completely lack forked, aggregation of the bundles does not occur so tha...