Hi, I just want to get initiated to the contexts of ( definitions and examples of ) spin structures on Riemann Surfaces . It would be great to have the answers and also some references for beginners'.
What is exactly the lifting of a simple closed curve $ \gamma $ in a closed oriented surface $ M $ to its unit tangent bundle $ UM $. How do you define it ? What exactly in 'framing' in this context ?
a) What exactly is the "intersection form" on $ H_1(M) $ ?
b) Why is it symplectic ? You can state an easy reference if there is one .
c) What is the symplectic automorphism group of $ H_1(M) $ ?
d) What is/are the definitions of spin structure on $ M $ ?