View Single Post
 Quote by kakarotyjn Thank you lavinia and zhentil! To lavinia,I'm not very clear about some property of Euler class you listed,my foundation of topology is quite insufficient.The derivation of the global angular form for an oriented 2 plane bundle :by$$\frac{d\theta_\alpha}{2\pi}-\pi^* \ksi_\alpha=\frac{d \theta_\beta}{2\pi}-\pi^*\ksi_\beta$$ where $$\theta$$ is angular coordinates and $$\ksi_\alpha$$ is a 1 form on $$U_\alpha$$,these forms piece together to give a global angular form on E^0. To zhentil,oh I'm sorry there are too many thing I don't know.what is transverse section?Why the intersection of the zero section with a transverse section represents a homology class?What is negative of the section ? Thank you again!