MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How do we construct Seifert fibration on mapping torus of surface with monodromy a periodic mapping class. I know that the fiber of the Seifert fibration has to be transverse to the surface fiber of the fibration over $S^1$ but I do not know how we do the construction. Under which conditions can we do the same construction for a reducible mapping class ?

I have another independent question: for a reducible mapping class, do the invariant multicurve corresponds to the set of splitting tori of the JSJ-decomposition.

share|cite|improve this question
up vote 4 down vote accepted

Just use the suspension flow of the periodic diffeomorphism $f: S\to S$ in the periodic mapping class. Then all flow lines will be periodic (i.e., circles) and you are done; the base will be the quotient $S/f$.

For the second question, the answer is yes; again, just suspend the invariant multicurve.

share|cite|improve this answer

Your Answer


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.