## Spin structures on Riemann surfaces and differential manifold [closed]

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'.

1. 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 ?

2. 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 $M$ ?

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Most of your questions have answers on Wikipedia. Have you looked there? Do you have any problems with its answers to your questions 1 and 2? Pretty much all your questions are answered on Wikipedia. – Ryan Budney Oct 27 2010 at 3:15
Have you looked at some textbook on the subject? All your questions should be answered in any of them. If you have specific problems with the definitions, ask in detail. but MO is generally thought not to be a place where one asks tell me about subject X questions. – Mariano Suárez-Alvarez Oct 27 2010 at 3:16