Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I would like to know more about relationships between the mapping class group of an orientable surface with negative Euler's characteristic and moduli spaces. In particular, I would like to have a rigorous explanation of the following three facts:

  1. having a family of surfaces given by a fibration $F\to E\to B$ (e.g. take B as $S^1$ and F as a compact surface of genus $g>1$), how to construct a map from $\pi_1(B)$ to $MCG(F)$.

  2. how point 1 should give a relation between the $MCG$ and the topological type of $E$

  3. how the cohomology of the $MCG$ is related with the cohomology of the moduli space of curves

In other words, I know just some chatting about that, but I would like to learn more deeply how to formulate and prove those facts.

Thanks a lot in advance, bye!

share|improve this question
2  
maybe math.utah.edu/~margalit/primer –  yoyo Jun 30 '11 at 15:53
    
Unfortunately it does not deal with that stuff. Thanks, anyway. –  fatoddsun Jun 30 '11 at 20:24

1 Answer 1

Just to leave answers as answers:

There is a new 500$+$ page book by Benson Farb and Dan Margalit called A Primer on Mapping Class Groups. I am not an expert in this area, but I'm not the polar opposite of one either, and the book looks to me to be very strong and likely to become a standard reference. So anyone who is at all interested in this subject would do well to download a copy of the book from the second author's webpage while free copies are still available (I have no reason to believe that a copy of this version of the book will go offline once the final version is published, but it doesn't hurt to be safe).

Added: the OP has made clear that his specific questions are not addressed in this book, so this is a very partial answer (more of an answer to the title than the question itself). I hope others will contribute more pertinent information.

share|improve this answer
    
Apparently your answer doesn't answer the question, as the OP left a comment indicating that his questions aren't addressed in that book. –  t.b. Jun 30 '11 at 20:47
    
Indeed, at least as far as I know, there's just a small part regarding surface bundles, but it's not enough to cover the three points that I have indicated. Anyway, it is a very good book..! –  fatoddsun Jun 30 '11 at 22:12

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.